error using fzero in line 6

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Nathaniel Asefa
Nathaniel Asefa on 11 Jun 2021
Commented: Star Strider on 11 Jun 2021
function hw7
close all
fun = @(e) hw7fun(e);
e0 = 0.05:0.025:1.25;
options = optimset('Display', 'iter');
[e, residual, exitflag, output] = fzero(fun, e0, options);
fprintf('exitflag %d residual %6.3e x %6.3f\n', exitflag, residual, e);
endu
function f = hw7fun(e)
dp=416;
L=1.5;
h=1e-3;
v=0.1;
d=5e-2;
p=2e3;
f = (dp/L)-150*((h*v)/d^2)*((1-e)^2/e^3)-(7/4)*((p*v^2)/d)*((1-e)/e^3);
endoutput.funcCount
end
%I cant figure out why there is an error

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Accepted Answer

Star Strider
Star Strider on 11 Jun 2021
Ran in:
Try something like this —
hw7 % Call Function
Func-count x f(x) Procedure 2 1.25 366.741 initial 3 1.24992 366.73 interpolation 4 1.24992 366.73 bisection 5 1.02643 294.435 interpolation 6 0.838192 84.7275 bisection 7 0.77936 -49.5456 interpolation 8 0.801069 5.98228 interpolation 9 0.79873 0.367892 interpolation 10 0.798578 -0.000226454 interpolation 11 0.798578 1.10962e-07 interpolation 12 0.798578 -5.68434e-14 interpolation 13 0.798578 -5.68434e-14 interpolation Zero found in the interval [0.05, 1.25] exitflag 1 residual -5.684e-14 x 0.799
function hw7
fun = @(e) hw7fun(e);
% e0 = 0.05:0.025:1.25;
e0 = [0.05 1.25];
options = optimset('Display', 'iter');
[e, residual, exitflag, output] = fzero(fun, e0, options);
fprintf('exitflag %d residual %6.3e x %6.3f\n', exitflag, residual, e);
function f = hw7fun(e)
dp=416;
L=1.5;
h=1e-3;
v=0.1;
d=5e-2;
p=2e3;
f = (dp/L)-150*((h*v)/d^2)*((1-e)^2/e^3)-(7/4)*((p*v^2)/d)*((1-e)/e^3);
% endoutput.funcCount
end
end
.
  2 Comments
Nathaniel Asefa
Nathaniel Asefa on 11 Jun 2021
i need it spaced by 0.025 is there any way I can keep it that way
Star Strider
Star Strider on 11 Jun 2021
Ran in:
Yes. Use a loop —
hw7 % Call Function
Search for an interval around 0.05 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.05 -5.36304e+06 0.05 -5.36304e+06 initial interval 3 0.0485858 -5.85392e+06 0.0514142 -4.92513e+06 search 5 0.048 -6.07465e+06 0.052 -4.75758e+06 search 7 0.0471716 -6.40598e+06 0.0528284 -4.53324e+06 search 9 0.046 -6.9166e+06 0.054 -4.23923e+06 search 11 0.0443431 -7.73478e+06 0.0556569 -3.86493e+06 search 13 0.042 -9.12545e+06 0.058 -3.40661e+06 search 15 0.0386863 -1.17178e+07 0.0613137 -2.87332e+06 search 17 0.034 -1.73465e+07 0.066 -2.29205e+06 search 19 0.0273726 -3.34734e+07 0.0726274 -1.70773e+06 search 21 0.018 -1.18859e+08 0.082 -1.17436e+06 search 23 0.00474517 -6.57608e+09 0.0952548 -738168 search 24 -0.014 2.60922e+08 0.0952548 -738168 search Search for a zero in the interval [-0.014, 0.0952548]: Func-count x f(x) Procedure 24 0.0952548 -738168 initial 25 0.0949466 -745639 interpolation 26 0.0404733 -1.0214e+07 bisection 27 -0.014 2.60922e+08 bisection 28 0.0132367 -3.00354e+08 interpolation 29 0.0132218 -3.01371e+08 interpolation 30 0.0059417 -3.34551e+09 bisection 31 0.00230164 -5.77676e+10 bisection 32 -0.00133842 2.94856e+11 bisection 33 -0.00125726 3.55696e+11 interpolation 34 0.000481607 -6.31707e+12 bisection 35 -0.000387827 1.21077e+13 interpolation 36 -0.000333065 1.91146e+13 interpolation 37 0.000183514 -1.14213e+14 bisection 38 0.000167152 -1.51145e+14 interpolation 39 -7.47752e-05 1.68875e+15 bisection 40 -5.17014e-05 5.1088e+15 interpolation 41 4.61885e-05 -7.16446e+15 bisection 42 4.61781e-05 -7.1693e+15 interpolation 43 2.17108e-05 -6.89871e+16 bisection 44 9.47716e-06 -8.29404e+17 bisection 45 3.36034e-06 -1.8606e+19 bisection 46 -2.75648e-06 3.37086e+19 bisection 47 -2.75247e-06 3.38563e+19 interpolation 48 -1.22527e-06 3.83805e+20 bisection 49 -4.61671e-07 7.17477e+21 bisection 50 3.01929e-07 -2.56503e+22 bisection 51 2.94989e-07 -2.75034e+22 interpolation 52 1.07559e-07 -5.67367e+23 bisection 53 -7.9871e-08 1.3856e+24 bisection 54 -7.93856e-08 1.41117e+24 interpolation 55 -3.27708e-08 2.00606e+25 bisection 56 1.3844e-08 -2.66086e+26 bisection 57 -9.46341e-09 8.33032e+26 interpolation 58 8.20148e-09 -1.27976e+27 interpolation 59 7.90729e-09 -1.42798e+27 interpolation 60 2.7044e-09 -3.56936e+28 bisection 61 -2.49848e-09 4.52663e+28 bisection 62 -2.4983e-09 4.52762e+28 interpolation 63 -1.19767e-09 4.10953e+29 bisection 64 -5.47355e-10 4.30523e+30 bisection 65 -2.22198e-10 6.43557e+31 bisection 66 1.0296e-10 -6.4684e+32 bisection 67 7.65273e-11 -1.57527e+33 interpolation 68 -5.96187e-11 3.33163e+33 bisection 69 -5.94251e-11 3.3643e+33 interpolation 70 -2.54854e-11 4.2651e+34 bisection 71 -8.51555e-12 1.14332e+36 bisection 72 8.45431e-12 -1.16834e+36 bisection 73 8.45386e-12 -1.16853e+36 interpolation 74 4.21162e-12 -9.45056e+36 bisection 75 2.0905e-12 -7.7278e+37 bisection 76 1.02994e-12 -6.46209e+38 bisection 77 4.99656e-13 -5.65967e+39 bisection 78 2.34516e-13 -5.47378e+40 bisection 79 1.01946e-13 -6.66338e+41 bisection 80 3.56609e-14 -1.55678e+43 bisection 81 -3.06242e-14 2.45817e+43 bisection 82 -3.01801e-14 2.56829e+43 interpolation 83 -1.38308e-14 2.66845e+44 bisection 84 -5.65624e-15 3.90141e+45 bisection 85 2.51837e-15 -4.42023e+46 bisection 86 1.72251e-15 -1.38141e+47 interpolation 87 -1.56893e-15 1.82807e+47 bisection 88 -1.12484e-15 4.96054e+47 interpolation 89 -5.24028e-16 4.90616e+48 bisection Current point x may be near a singular point. The interval [-0.014, 0.0952548] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 4.906e+48 x -0.000 Search for an interval around 0.075 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.075 -1.54671e+06 0.075 -1.54671e+06 initial interval 3 0.0728787 -1.68966e+06 0.0771213 -1.41924e+06 search 5 0.072 -1.75396e+06 0.078 -1.37049e+06 search 7 0.0707574 -1.85052e+06 0.0792426 -1.30523e+06 search 9 0.069 -1.99937e+06 0.081 -1.21974e+06 search 11 0.0665147 -2.238e+06 0.0834853 -1.11096e+06 search 13 0.063 -2.6439e+06 0.087 -977852 search 15 0.0580294 -3.40132e+06 0.0919706 -823137 search 17 0.051 -5.04834e+06 0.099 -654748 search 19 0.0410589 -9.77714e+06 0.108941 -485831 search 21 0.027 -3.48918e+07 0.123 -332103 search 23 0.00711775 -1.94378e+09 0.142882 -206919 search 24 -0.021 7.78487e+07 0.142882 -206919 search Search for a zero in the interval [-0.021, 0.142882]: Func-count x f(x) Procedure 24 0.142882 -206919 initial 25 0.142448 -208928 interpolation 26 0.0607239 -2.95974e+06 bisection 27 -0.021 7.78487e+07 bisection 28 0.019862 -8.82981e+07 interpolation 29 0.0198447 -8.85303e+07 interpolation 30 0.00899536 -9.61151e+08 bisection 31 0.00357069 -1.54519e+10 bisection 32 -0.00185398 1.10995e+11 bisection 33 -0.00160849 1.69923e+11 interpolation 34 0.000858358 -1.11538e+12 bisection 35 0.000763486 -1.58514e+12 interpolation 36 -0.000375067 1.33857e+13 bisection 37 -0.000305634 2.47362e+13 interpolation 38 0.000194209 -9.63626e+13 bisection 39 0.000188447 -1.05476e+14 interpolation 40 6.63673e-05 -2.41498e+15 bisection 41 -5.57123e-05 4.08296e+15 bisection 42 -5.5659e-05 4.09471e+15 interpolation 43 -2.51658e-05 4.42982e+16 bisection 44 -9.91913e-06 7.23417e+17 bisection 45 5.3275e-06 -4.66909e+18 bisection 46 4.76263e-06 -6.53525e+18 interpolation 47 -2.29581e-06 5.83439e+19 bisection 48 -1.82203e-06 1.16719e+20 interpolation 49 1.23341e-06 -3.76257e+20 bisection 50 1.21293e-06 -3.95637e+20 interpolation 51 4.5931e-07 -7.28594e+21 bisection 52 -2.9431e-07 2.76944e+22 bisection 53 -2.86188e-07 3.01196e+22 interpolation 54 -1.01844e-07 6.68341e+23 bisection 55 8.25004e-08 -1.25729e+24 bisection 56 8.23522e-08 -1.2641e+24 interpolation 57 3.63402e-08 -1.4711e+25 bisection 58 1.33342e-08 -2.97786e+26 bisection 59 -9.67179e-09 7.80341e+26 bisection 60 -9.59424e-09 7.99416e+26 interpolation 61 -3.88152e-09 1.20726e+28 bisection 62 1.8312e-09 -1.14973e+29 bisection 63 1.40485e-09 -2.54632e+29 interpolation 64 -1.02516e-09 6.5529e+29 bisection 65 -1.01749e-09 6.70217e+29 interpolation 66 -4.13821e-10 9.96249e+30 bisection 67 1.89848e-10 -1.03179e+32 bisection 68 1.38446e-10 -2.66049e+32 interpolation 69 -1.11987e-10 5.02697e+32 bisection 70 -1.1178e-10 5.05483e+32 interpolation 71 -4.92753e-11 5.90087e+33 bisection 72 -1.80228e-11 1.20598e+35 bisection 73 1.32298e-11 -3.04889e+35 bisection 74 1.31375e-11 -3.11363e+35 interpolation 75 5.37052e-12 -4.55781e+36 bisection 76 -2.39646e-12 5.12971e+37 bisection 77 -1.64756e-12 1.57863e+38 interpolation 78 1.48703e-12 -2.14708e+38 bisection 79 1.48658e-12 -2.149e+38 interpolation 80 7.03159e-13 -2.03069e+39 bisection 81 3.11446e-13 -2.33698e+40 bisection 82 1.1559e-13 -4.57132e+41 bisection 83 -8.0266e-14 1.36524e+42 bisection 84 -7.92336e-14 1.41931e+42 interpolation 85 -3.07858e-14 2.41967e+43 bisection 86 1.76621e-14 -1.28138e+44 bisection 87 1.64805e-14 -1.57722e+44 interpolation 88 -6.56182e-15 2.4988e+45 bisection 89 4.95935e-15 -5.78804e+45 interpolation 90 3.39478e-15 -1.80456e+46 interpolation 91 -3.08774e-15 2.39817e+46 bisection 92 -2.64366e-15 3.82111e+46 interpolation 93 -1.24507e-15 3.65783e+47 bisection 94 -5.45777e-16 4.34269e+48 bisection Current point x may be near a singular point. The interval [-0.021, 0.142882] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 4.343e+48 x -0.000 Search for an interval around 0.1 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.1 -634583 0.1 -634583 initial interval 3 0.0971716 -693841 0.102828 -581774 search 5 0.096 -720506 0.104 -561583 search 7 0.0943431 -760555 0.105657 -534565 search 9 0.092 -822320 0.108 -499181 search 11 0.0886863 -921393 0.111314 -454183 search 13 0.084 -1.09004e+06 0.116 -399166 search 15 0.0773726 -1.40507e+06 0.122627 -335285 search 17 0.068 -2.09115e+06 0.132 -265866 search 19 0.0547452 -4.06522e+06 0.145255 -196381 search 21 0.036 -1.45825e+07 0.164 -133343 search 23 0.00949033 -8.18058e+08 0.19051 -82243.1 search 24 -0.028 3.30697e+07 0.19051 -82243.1 search Search for a zero in the interval [-0.028, 0.19051]: Func-count x f(x) Procedure 24 0.19051 -82243.1 initial 25 0.189968 -83007.7 interpolation 26 0.0809838 -1.22049e+06 bisection 27 -0.028 3.30697e+07 bisection 28 0.0264919 -3.69576e+07 interpolation 29 0.0264744 -3.70316e+07 interpolation 30 0.0121038 -3.9328e+08 bisection 31 0.00491855 -5.90382e+09 bisection 32 -0.00226673 6.07568e+10 bisection 33 -0.00166579 1.52992e+11 interpolation 34 0.00132591 -3.0247e+11 bisection 35 0.00132277 -3.04629e+11 interpolation 36 0.000576415 -3.68423e+12 bisection 37 0.000203236 -8.40837e+13 bisection 38 -0.000169942 1.43872e+14 bisection 39 -0.000169767 1.44318e+14 interpolation 40 -7.65599e-05 1.57338e+15 bisection 41 -2.99564e-05 2.62633e+16 bisection 42 1.66471e-05 -1.53032e+17 bisection 43 1.5248e-05 -1.99141e+17 interpolation 44 -6.65466e-06 2.39569e+18 bisection 45 -4.33208e-06 8.68395e+18 interpolation 46 4.29666e-06 -8.90038e+18 bisection 47 4.29666e-06 -8.90038e+18 interpolation 48 2.13948e-06 -7.20908e+19 bisection 49 1.06089e-06 -5.91287e+20 bisection 50 5.21589e-07 -4.97529e+21 bisection 51 2.51941e-07 -4.41476e+22 bisection 52 1.17117e-07 -4.39485e+23 bisection 53 4.9705e-08 -5.74915e+24 bisection 54 -1.7707e-08 1.27165e+26 bisection 55 1.5999e-08 -1.72396e+26 interpolation 56 1.58148e-08 -1.78489e+26 interpolation 57 6.20809e-09 -2.95075e+27 bisection 58 -3.39865e-09 1.7984e+28 bisection 59 -3.08186e-09 2.41193e+28 interpolation 60 1.40472e-09 -2.54705e+29 bisection 61 1.01119e-09 -6.8281e+29 interpolation 62 -8.38572e-10 1.19725e+30 bisection 63 -8.37565e-10 1.20157e+30 interpolation 64 -3.75627e-10 1.33209e+31 bisection 65 -1.44658e-10 2.33227e+32 bisection 66 8.63113e-11 -1.098e+33 bisection 67 8.20177e-11 -1.27962e+33 interpolation 68 -2.91732e-11 2.84349e+34 bisection 69 2.64222e-11 -3.82733e+34 interpolation 70 2.61409e-11 -3.95223e+34 interpolation 71 1.03328e-11 -6.39951e+35 bisection 72 -5.47525e-12 4.30123e+36 bisection 73 -4.84071e-12 6.22413e+36 interpolation 74 2.42879e-12 -4.9276e+37 bisection 75 2.03237e-12 -8.40995e+37 interpolation 76 -1.20596e-12 4.02538e+38 bisection 77 -1.14334e-12 4.7236e+38 interpolation 78 4.13208e-13 -1.00069e+40 bisection 79 -3.65068e-13 1.45105e+40 interpolation 80 -3.56955e-13 1.55226e+40 interpolation 81 -1.30702e-13 3.16197e+41 bisection 82 9.55508e-14 -8.09285e+41 bisection 83 9.48511e-14 -8.27327e+41 interpolation 84 3.86378e-14 -1.22397e+43 bisection 85 -1.75756e-14 1.30039e+44 bisection 86 -1.25997e-14 3.5296e+44 interpolation 87 1.05311e-14 -6.04488e+44 bisection 88 1.0087e-14 -6.87894e+44 interpolation 89 4.52633e-15 -7.61316e+45 bisection 90 1.74601e-15 -1.32636e+47 bisection 91 -1.03431e-15 6.38049e+47 bisection 92 -5.9022e-16 3.43371e+48 interpolation 93 3.55852e-16 -1.56674e+49 bisection Current point x may be near a singular point. The interval [-0.028, 0.19051] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual -1.567e+49 x 0.000 Search for an interval around 0.125 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.125 -315675 0.125 -315675 initial interval 3 0.121464 -345477 0.128536 -289130 search 5 0.12 -358893 0.13 -278986 search 7 0.117929 -379048 0.132071 -265414 search 9 0.115 -410144 0.135 -247648 search 11 0.110858 -460050 0.139142 -225067 search 13 0.105 -545069 0.145 -197479 search 15 0.0967157 -704060 0.153284 -165484 search 17 0.085 -1.05085e+06 0.165 -130771 search 19 0.0684315 -2.05088e+06 0.181569 -96104.4 search 21 0.045 -7.39585e+06 0.205 -64758.5 search 23 0.0118629 -4.17834e+08 0.238137 -39471.2 search 24 -0.035 1.70481e+07 0.238137 -39471.2 search Search for a zero in the interval [-0.035, 0.238137]: Func-count x f(x) Procedure 24 0.238137 -39471.2 initial 25 0.237506 -39822.2 interpolation 26 0.101253 -610445 bisection 27 -0.035 1.70481e+07 bisection 28 0.0331265 -1.87723e+07 interpolation 29 0.0331104 -1.88002e+07 interpolation 30 0.015267 -1.95345e+08 bisection 31 0.00634536 -2.74567e+09 bisection 32 -0.0025763 4.13943e+10 bisection 33 0.00188453 -1.05286e+11 interpolation 34 -0.00131742 3.09176e+11 interpolation 35 0.00107114 -5.73854e+11 bisection 36 0.00106933 -5.76773e+11 interpolation 37 0.000473092 -6.66441e+12 bisection 38 0.000174974 -1.31767e+14 bisection 39 -0.000123143 3.78118e+14 bisection 40 -0.000121766 3.91088e+14 interpolation 41 -4.79255e-05 6.41396e+15 bisection 42 2.59155e-05 -4.05615e+16 bisection 43 2.32895e-05 -5.58873e+16 interpolation 44 -1.1005e-05 5.29715e+17 bisection 45 -8.46517e-06 1.16386e+18 interpolation 46 6.14227e-06 -3.0466e+18 bisection 47 6.09322e-06 -3.12077e+18 interpolation 48 2.46588e-06 -4.70854e+19 bisection 49 -1.16145e-06 4.5061e+20 bisection 50 -8.88604e-07 1.00619e+21 interpolation 51 6.52215e-07 -2.54467e+21 bisection 52 6.47658e-07 -2.59877e+21 interpolation 53 2.64732e-07 -3.80528e+22 bisection 54 -1.18194e-07 4.27579e+23 bisection 55 -8.13595e-08 1.31093e+24 interpolation 56 7.32687e-08 -1.79493e+24 bisection 57 7.32557e-08 -1.79589e+24 interpolation 58 3.46052e-08 -1.70366e+25 bisection 59 1.52799e-08 -1.979e+26 bisection 60 5.61724e-09 -3.98323e+27 bisection 61 -4.0454e-09 1.0664e+28 bisection 62 -4.01023e-09 1.0947e+28 interpolation 63 -1.61216e-09 1.68493e+29 bisection 64 7.85919e-10 -1.45436e+30 bisection 65 6.33854e-10 -2.77228e+30 interpolation 66 -4.13119e-10 1.00133e+31 bisection 67 -4.03324e-10 1.07607e+31 interpolation 68 -1.46478e-10 2.24638e+32 bisection 69 1.10367e-10 -5.25147e+32 bisection 70 1.09808e-10 -5.3322e+32 interpolation 71 4.58761e-11 -7.31216e+33 bisection 72 -1.80555e-11 1.19944e+35 bisection 73 1.39103e-11 -2.62298e+35 interpolation 74 1.0377e-11 -6.31809e+35 interpolation 75 -8.02493e-12 1.3661e+36 bisection 76 -7.99606e-12 1.38095e+36 interpolation 77 -3.41e-12 1.78049e+37 bisection 78 1.17605e-12 -4.34037e+38 bisection 79 -1.11698e-12 5.06608e+38 interpolation 80 -1.11552e-12 5.08591e+38 interpolation 81 -4.98767e-13 5.68999e+39 bisection 82 -1.90389e-13 1.02301e+41 bisection 83 1.17989e-13 -4.29809e+41 bisection 84 1.13662e-13 -4.80799e+41 interpolation 85 3.87309e-14 -1.21515e+43 bisection 86 -3.61997e-14 1.4883e+43 bisection 87 -3.57556e-14 1.54445e+43 interpolation 88 -1.7245e-14 1.37663e+44 bisection 89 -7.98967e-15 1.38426e+45 bisection 90 -3.36201e-15 1.85783e+46 bisection 91 1.26564e-15 -3.48237e+47 bisection 92 -1.04819e-15 6.13039e+47 interpolation 93 -6.04098e-16 3.20245e+48 interpolation 94 4.2742e-16 -9.04148e+48 bisection Current point x may be near a singular point. The interval [-0.035, 0.238137] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual -9.041e+48 x 0.000 Search for an interval around 0.15 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.15 -177303 0.15 -177303 initial interval 3 0.145757 -194239 0.154243 -162228 search 5 0.144 -201866 0.156 -156469 search 7 0.141515 -213327 0.158485 -148767 search 9 0.138 -231017 0.162 -138688 search 11 0.133029 -259424 0.166971 -125885 search 13 0.126 -307856 0.174 -110256 search 15 0.116059 -398531 0.183941 -92152.1 search 17 0.102 -596626 0.198 -72542.9 search 19 0.0821177 -1.16916e+06 0.217882 -53007.8 search 21 0.054 -4.23923e+06 0.246 -35405.7 search 23 0.0142355 -2.41216e+08 0.285765 -21278.5 search 24 -0.042 9.93326e+06 0.285765 -21278.5 search Search for a zero in the interval [-0.042, 0.285765]: Func-count x f(x) Procedure 24 0.285765 -21278.5 initial 25 0.285064 -21459.3 interpolation 26 0.121532 -344875 bisection 27 -0.042 9.93326e+06 bisection 28 0.039766 -1.07768e+07 interpolation 29 0.039752 -1.07883e+07 interpolation 30 0.0184849 -1.09693e+08 bisection 31 0.00785137 -1.44716e+09 bisection 32 -0.00278219 3.28747e+10 bisection 33 0.00253459 -4.32484e+10 interpolation 34 0.0025135 -4.43473e+10 interpolation 35 0.00101371 -6.77041e+11 bisection 36 -0.000486071 6.15062e+12 bisection 37 -0.00038263 1.26077e+13 interpolation 38 0.000263821 -3.84379e+13 bisection 39 0.000260174 -4.00773e+13 interpolation 40 0.000100385 -6.97839e+14 bisection 41 -5.94042e-05 3.36806e+15 bisection 42 -5.62544e-05 3.96606e+15 interpolation 43 2.04904e-05 -8.20629e+16 bisection 44 -1.7882e-05 1.2347e+17 interpolation 45 -1.73382e-05 1.35456e+17 interpolation 46 -6.08437e-06 3.13444e+18 bisection 47 5.16949e-06 -5.11046e+18 bisection 48 5.16559e-06 -5.12203e+18 interpolation 49 2.35408e-06 -5.41181e+19 bisection 50 9.48317e-07 -8.27835e+20 bisection 51 -4.57441e-07 7.37563e+21 bisection 52 -3.634e-07 1.47113e+22 interpolation 53 2.45438e-07 -4.77507e+22 bisection 54 2.41271e-07 -5.02676e+22 interpolation 55 9.11452e-08 -9.32402e+23 bisection 56 -5.89808e-08 3.4409e+24 bisection 57 -5.74893e-08 3.71572e+24 interpolation 58 -2.07036e-08 7.95552e+25 bisection 59 1.60822e-08 -1.69734e+26 bisection 60 1.60278e-08 -1.71468e+26 interpolation 61 6.85855e-09 -2.1883e+27 bisection 62 -2.31069e-09 5.7224e+28 bisection 63 2.27393e-09 -6.00446e+28 interpolation 64 2.27385e-09 -6.00509e+28 interpolation 65 1.10017e-09 -5.30189e+29 bisection 66 5.13323e-10 -5.21953e+30 bisection 67 2.19902e-10 -6.63919e+31 bisection 68 -7.35187e-11 1.77669e+33 bisection 69 7.31919e-11 -1.8006e+33 interpolation 70 7.31914e-11 -1.80063e+33 interpolation 71 3.62689e-11 -1.4798e+34 bisection 72 1.78076e-11 -1.25022e+35 bisection 73 8.577e-12 -1.11892e+36 bisection 74 3.96168e-12 -1.13544e+37 bisection 75 1.65402e-12 -1.5602e+38 bisection 76 -6.53634e-13 2.52814e+39 bisection 77 5.00195e-13 -5.64139e+39 interpolation 78 3.62769e-13 -1.47881e+40 interpolation 79 -2.9657e-13 2.70661e+40 bisection 80 -2.96112e-13 2.71918e+40 interpolation 81 -1.31506e-13 3.10433e+41 bisection 82 -4.92031e-14 5.92688e+42 bisection 83 3.30998e-14 -1.94684e+43 bisection 84 3.25158e-14 -2.05362e+43 interpolation 85 1.22321e-14 -3.85748e+44 bisection 86 -8.05168e-15 1.35252e+45 bisection 87 -7.60759e-15 1.60348e+45 interpolation 88 -2.7587e-15 3.36274e+46 bisection 89 2.0902e-15 -7.73109e+46 bisection 90 1.64611e-15 -1.5828e+47 interpolation 91 6.55932e-16 -2.50166e+48 bisection 92 -3.34247e-16 1.8906e+49 bisection Current point x may be near a singular point. The interval [-0.042, 0.285765] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 1.891e+49 x -0.000 Search for an interval around 0.175 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.175 -108240 0.175 -108240 initial interval 3 0.17005 -118709 0.17995 -98926.1 search 5 0.168 -123426 0.182 -95369.7 search 7 0.165101 -130515 0.184899 -90614.7 search 9 0.161 -141463 0.189 -84395.1 search 11 0.155201 -159054 0.194799 -76499.3 search 13 0.147 -189070 0.203 -66869.4 search 15 0.135402 -245331 0.214598 -55727.7 search 17 0.119 -368446 0.231 -43681 search 19 0.095804 -725097 0.254196 -31710.5 search 21 0.063 -2.6439e+06 0.287 -20964.3 search 23 0.0166081 -1.51534e+08 0.333392 -12386.9 search 24 -0.049 6.29784e+06 0.333392 -12386.9 search Search for a zero in the interval [-0.049, 0.333392]: Func-count x f(x) Procedure 24 0.333392 -12386.9 initial 25 0.332641 -12487.2 interpolation 26 0.141821 -211871 bisection 27 -0.049 6.29784e+06 bisection 28 0.0464103 -6.73183e+06 interpolation 29 0.0463991 -6.7368e+06 interpolation 30 0.0217576 -6.70399e+07 bisection 31 0.00943693 -8.32069e+08 bisection 32 0.00327657 -2.00036e+10 bisection 33 -0.00288379 2.95241e+10 bisection 34 -0.00288281 2.95541e+10 interpolation 35 -0.00134321 2.91718e+11 bisection 36 -0.000573407 3.74685e+12 bisection 37 0.000196394 -9.31829e+13 bisection 38 -0.000188507 1.05416e+14 interpolation 39 -0.000188387 1.05618e+14 interpolation 40 -8.62945e-05 1.09874e+15 bisection 41 -3.52484e-05 1.61214e+16 bisection 42 1.57977e-05 -1.79068e+17 bisection 43 1.09695e-05 -5.34863e+17 interpolation 44 -9.72535e-06 7.67526e+17 bisection 45 -9.72264e-06 7.68167e+17 interpolation 46 -4.55029e-06 7.49357e+18 bisection 47 -1.96412e-06 9.31761e+19 bisection 48 -6.71027e-07 2.3366e+21 bisection 49 6.22061e-07 -2.93295e+21 bisection 50 6.22022e-07 -2.93351e+21 interpolation 51 2.9877e-07 -2.64725e+22 bisection 52 1.37143e-07 -2.73704e+23 bisection 53 5.63303e-08 -3.94984e+24 bisection 54 -2.44828e-08 4.81083e+25 bisection 55 1.59237e-08 -1.74853e+26 interpolation 56 -1.57643e-08 1.8021e+26 interpolation 57 -1.57642e-08 1.80215e+26 interpolation 58 -7.7227e-09 1.53284e+27 bisection 59 -3.70196e-09 1.39158e+28 bisection 60 -1.69159e-09 1.45854e+29 bisection 61 -6.86405e-10 2.18305e+30 bisection 62 3.1878e-10 -2.17937e+31 bisection 63 2.37928e-10 -5.24167e+31 interpolation 64 -1.83812e-10 1.13679e+32 bisection 65 -1.83142e-10 1.14932e+32 interpolation 66 -7.8042e-11 1.48532e+33 bisection 67 2.70577e-11 -3.56395e+34 bisection 68 -2.54922e-11 4.26172e+34 interpolation 69 -2.54395e-11 4.28823e+34 interpolation 70 -1.1157e-11 5.08352e+35 bisection 71 -4.01571e-12 1.09023e+37 bisection 72 3.12555e-12 -2.31219e+37 bisection 73 3.11527e-12 -2.33516e+37 interpolation 74 1.3351e-12 -2.96665e+38 bisection 75 -4.45079e-13 8.00743e+39 bisection 76 4.45009e-13 -8.01121e+39 interpolation 77 4.44565e-13 -8.03524e+39 interpolation 78 2.22213e-13 -6.43427e+40 bisection 79 1.11036e-13 -5.15715e+41 bisection 80 5.54482e-14 -4.14136e+42 bisection 81 2.76541e-14 -3.33831e+43 bisection 82 1.37571e-14 -2.71161e+44 bisection 83 6.80855e-15 -2.23687e+45 bisection 84 3.33429e-15 -1.90455e+46 bisection 85 1.59716e-15 -1.73283e+47 bisection 86 7.286e-16 -1.82531e+48 bisection Current point x may be near a singular point. The interval [-0.049, 0.333392] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual -1.825e+48 x 0.000 Search for an interval around 0.2 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.2 -70202.7 0.2 -70202.7 initial interval 3 0.194343 -77084.9 0.205657 -64083.8 search 5 0.192 -80186.9 0.208 -61748.3 search 7 0.188686 -84851.3 0.211314 -58626.7 search 9 0.184 -92056.7 0.216 -54545.5 search 11 0.177373 -103641 0.222627 -49367.7 search 13 0.168 -123426 0.232 -43058.3 search 15 0.154745 -160554 0.245255 -35767.8 search 17 0.136 -241937 0.264 -27899.7 search 19 0.10949 -478255 0.29051 -20102.3 search 21 0.072 -1.75396e+06 0.328 -13129.9 search 23 0.0189807 -1.01269e+08 0.381019 -7597.33 search 24 -0.056 4.24756e+06 0.381019 -7597.33 search Search for a zero in the interval [-0.056, 0.381019]: Func-count x f(x) Procedure 24 0.381019 -7597.33 initial 25 0.380239 -7655.95 interpolation 26 0.16212 -138361 bisection 27 -0.056 4.24756e+06 bisection 28 0.0530598 -4.4731e+06 interpolation 29 0.0530513 -4.47528e+06 interpolation 30 0.0250855 -4.35923e+07 bisection 31 0.0111025 -5.10092e+08 bisection 32 0.00411107 -1.0119e+10 bisection 33 -0.0028804 2.96283e+10 bisection 34 -0.00284653 3.06975e+10 interpolation 35 -0.0011156 5.09061e+11 bisection 36 0.000615334 -3.02833e+12 bisection 37 0.000560904 -3.99847e+12 interpolation 38 -0.000250132 4.51238e+13 bisection 39 -0.00017169 1.39523e+14 interpolation 40 0.000155386 -1.88149e+14 bisection 41 0.000155362 -1.88235e+14 interpolation 42 7.36051e-05 -1.77031e+15 bisection 43 3.27266e-05 -2.01414e+16 bisection 44 1.22873e-05 -3.80566e+17 bisection 45 -8.15197e-06 1.30323e+18 bisection 46 -7.98788e-06 1.3852e+18 interpolation 47 -2.96011e-06 2.72197e+19 bisection 48 2.06767e-06 -7.98661e+19 bisection 49 2.04265e-06 -8.28364e+19 interpolation 50 7.98215e-07 -1.38818e+21 bisection 51 -4.46221e-07 7.94612e+21 bisection 52 -4.1025e-07 1.02249e+22 interpolation 53 1.75997e-07 -1.29506e+23 bisection 54 -1.17127e-07 4.39377e+23 interpolation 55 1.09268e-07 -5.41164e+23 interpolation 56 1.089e-07 -5.46671e+23 interpolation 57 4.66097e-08 -6.97228e+24 bisection 58 -1.56801e-08 1.83129e+26 bisection 59 1.54648e-08 -1.90885e+26 interpolation 60 1.54645e-08 -1.90898e+26 interpolation 61 7.51692e-09 -1.66221e+27 bisection 62 3.54315e-09 -1.58721e+28 bisection 63 1.55627e-09 -1.87305e+29 bisection 64 5.62828e-10 -3.95984e+30 bisection 65 -4.30614e-10 8.8418e+30 bisection 66 -4.28823e-10 8.95302e+30 interpolation 67 -1.81358e-10 1.18357e+32 bisection 68 6.6107e-11 -2.44378e+33 bisection 69 -5.76256e-11 3.68943e+33 interpolation 70 -5.58241e-11 4.05826e+33 interpolation 71 -1.95092e-11 9.50791e+34 bisection 72 1.68056e-11 -1.48744e+35 bisection 73 1.67962e-11 -1.48995e+35 interpolation 74 7.7222e-12 -1.53314e+36 bisection 75 3.1852e-12 -2.18471e+37 bisection 76 -1.35179e-12 2.85809e+38 bisection 77 9.16706e-13 -9.16461e+38 interpolation 78 -8.12515e-13 1.31617e+39 interpolation 79 -7.95959e-13 1.40001e+39 interpolation 80 -2.94536e-13 2.76305e+40 bisection 81 2.06887e-13 -7.97273e+40 bisection 82 2.04526e-13 -8.25199e+40 interpolation 83 8.03507e-14 -1.36093e+42 bisection 84 -4.38248e-14 8.38775e+42 bisection 85 -3.96348e-14 1.1339e+43 interpolation 86 1.82629e-14 -1.15902e+44 bisection 87 1.34317e-14 -2.91347e+44 interpolation 88 -1.06859e-14 5.78588e+44 bisection 89 -1.02418e-14 6.57162e+44 interpolation 90 -4.43446e-15 8.09621e+45 bisection 91 -1.53078e-15 1.96818e+47 bisection 92 1.3729e-15 -2.72827e+47 bisection 93 9.28811e-16 -8.81096e+47 interpolation 94 4.24935e-16 -9.20104e+48 bisection Current point x may be near a singular point. The interval [-0.056, 0.381019] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual -9.201e+48 x 0.000 Search for an interval around 0.225 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.225 -47665.9 0.225 -47665.9 initial interval 3 0.218636 -52407.4 0.231364 -43453.1 search 5 0.216 -54545.5 0.234 -41845.9 search 7 0.212272 -57761.4 0.237728 -39698.3 search 9 0.207 -62731.6 0.243 -36891.9 search 11 0.199544 -70727.5 0.250456 -33333.8 search 13 0.189 -84395.1 0.261 -29002.1 search 15 0.174088 -110076 0.275912 -24003.7 search 17 0.153 -166466 0.297 -18619.7 search 19 0.123177 -330608 0.326823 -13299.1 search 21 0.081 -1.21974e+06 0.369 -8561.42 search 23 0.0213532 -7.0951e+07 0.428647 -4825.67 search 24 -0.063 3.00323e+06 0.428647 -4825.67 search Search for a zero in the interval [-0.063, 0.428647]: Func-count x f(x) Procedure 24 0.428647 -4825.67 initial 25 0.427858 -4861.06 interpolation 26 0.182429 -94646.4 bisection 27 -0.063 3.00323e+06 bisection 28 0.0597145 -3.11577e+06 interpolation 29 0.0597087 -3.11671e+06 interpolation 30 0.0284687 -2.972e+07 bisection 31 0.0128487 -3.28518e+08 bisection 32 0.00503876 -5.49063e+09 bisection 33 -0.00277123 3.3266e+10 bisection 34 -0.00252004 4.42269e+10 interpolation 35 0.00113376 -4.83881e+11 bisection 36 0.000794473 -1.40676e+12 interpolation 37 -0.000693135 2.12155e+12 bisection 38 -0.000692845 2.12422e+12 interpolation 39 -0.000321088 2.1334e+13 bisection 40 -0.00013521 2.85654e+14 bisection 41 5.06687e-05 -5.42704e+15 bisection 42 -4.22705e-05 9.34785e+15 interpolation 43 -3.89519e-05 1.19464e+16 interpolation 44 1.65308e-05 -1.56286e+17 bisection 45 -1.12106e-05 5.01102e+17 interpolation 46 9.9356e-06 -7.1981e+17 interpolation 47 9.73275e-06 -7.65763e+17 interpolation 48 3.60062e-06 -1.51241e+19 bisection 49 -2.5315e-06 4.35184e+19 bisection 50 -2.5029e-06 4.50273e+19 interpolation 51 -9.84168e-07 7.40624e+20 bisection 52 5.34563e-07 -4.62177e+21 bisection 53 4.81997e-07 -6.30481e+21 interpolation 54 -2.24803e-07 6.21443e+22 bisection 55 -1.69079e-07 1.46061e+23 interpolation 56 1.28597e-07 -3.31979e+23 bisection 57 1.28019e-07 -3.36497e+23 interpolation 58 5.3889e-08 -4.51133e+24 bisection 59 -2.02411e-08 8.51344e+25 bisection 60 1.6824e-08 -1.48258e+26 interpolation 61 1.54129e-08 -1.9282e+26 interpolation 62 -6.72089e-09 2.32554e+27 bisection 63 -4.36543e-09 8.48642e+27 interpolation 64 4.346e-09 -8.60074e+27 bisection 65 4.346e-09 -8.60074e+27 interpolation 66 2.16814e-09 -6.92694e+28 bisection 67 1.07921e-09 -5.61671e+29 bisection 68 5.3475e-10 -4.61692e+30 bisection 69 2.62518e-10 -3.90236e+31 bisection 70 1.26402e-10 -3.49576e+32 bisection 71 5.83441e-11 -3.5548e+33 bisection 72 2.4315e-11 -4.91111e+34 bisection 73 -9.71396e-12 7.70222e+35 bisection 74 7.30054e-12 -1.81443e+36 interpolation 75 4.85589e-12 -6.16593e+36 interpolation 76 -4.64366e-12 7.05057e+36 bisection 77 -4.64321e-12 7.05259e+36 interpolation 78 -2.26855e-12 6.04729e+37 bisection 79 -1.08122e-12 5.58556e+38 bisection 80 -4.8755e-13 6.09181e+39 bisection 81 -1.90717e-13 1.01774e+41 bisection 82 1.06116e-13 -5.90833e+41 bisection 83 9.72746e-14 -7.6702e+41 interpolation 84 -4.23007e-14 9.32741e+42 bisection 85 2.74869e-14 -3.39959e+43 interpolation 86 -2.72756e-14 3.47921e+43 interpolation 87 -2.68315e-14 3.65484e+43 interpolation 88 -1.32045e-14 3.06649e+44 bisection 89 -6.39094e-15 2.70465e+45 bisection 90 -2.98417e-15 2.65664e+46 bisection 91 -1.28079e-15 3.36023e+47 bisection 92 -4.29101e-16 8.93565e+48 bisection Current point x may be near a singular point. The interval [-0.063, 0.428647] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 8.936e+48 x -0.000 Search for an interval around 0.25 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.25 -33538.7 0.25 -33538.7 initial interval 3 0.242929 -36928.1 0.257071 -30529.2 search 5 0.24 -38457.2 0.26 -29381.6 search 7 0.235858 -40757.8 0.264142 -27848.8 search 9 0.23 -44315.2 0.27 -25846.6 search 11 0.221716 -50041.9 0.278284 -23309.9 search 13 0.21 -59839.8 0.29 -20224.7 search 15 0.193431 -78273.4 0.306569 -16669.7 search 17 0.17 -118822 0.33 -12848.2 search 19 0.136863 -237145 0.363137 -9083.11 search 21 0.09 -880338 0.41 -5745.34 search 23 0.0237258 -5.15967e+07 0.476274 -3131.27 search 24 -0.07 2.20398e+06 0.476274 -3131.27 search Search for a zero in the interval [-0.07, 0.476274]: Func-count x f(x) Procedure 24 0.476274 -3131.27 initial 25 0.475499 -3153.05 interpolation 26 0.20275 -67139.8 bisection 27 -0.07 2.20398e+06 bisection 28 0.0663748 -2.25252e+06 interpolation 29 0.0663711 -2.2529e+06 interpolation 30 0.0319079 -2.10331e+07 bisection 31 0.0146763 -2.20031e+08 bisection 32 0.00606044 -3.15232e+09 bisection 33 -0.00255537 4.24188e+10 bisection 34 0.00175253 -1.3093e+11 interpolation 35 -0.00150122 2.08991e+11 interpolation 36 -0.00143011 2.41726e+11 interpolation 37 0.000499261 -5.67027e+12 bisection 38 -0.000465424 7.00586e+12 interpolation 39 -0.000463785 7.08041e+12 interpolation 40 -0.000198023 9.0938e+13 bisection 41 6.7739e-05 -2.27122e+15 bisection 42 -6.51419e-05 2.55418e+15 interpolation 43 -6.51063e-05 2.55838e+15 interpolation 44 -2.99559e-05 2.62647e+16 bisection 45 -1.23807e-05 3.7203e+17 bisection 46 5.19454e-06 -5.03686e+18 bisection 47 -3.59306e-06 1.52199e+19 interpolation 48 3.0095e-06 -2.59011e+19 interpolation 49 2.79011e-06 -3.25043e+19 interpolation 50 -1.14929e-06 4.65073e+20 bisection 51 8.20411e-07 -1.27853e+21 interpolation 52 -6.23906e-07 2.90702e+21 interpolation 53 -4.39947e-07 8.29091e+21 interpolation 54 3.79227e-07 -1.29451e+22 bisection 55 3.79017e-07 -1.29667e+22 interpolation 56 1.74328e-07 -1.3326e+23 bisection 57 7.19842e-08 -1.89275e+24 bisection 58 -3.03602e-08 2.52286e+25 bisection 59 2.0812e-08 -7.83183e+25 interpolation 60 -1.78924e-08 1.23254e+26 interpolation 61 -1.71229e-08 1.40628e+26 interpolation 62 5.77391e-09 -3.66771e+27 bisection 63 -5.67451e-09 3.86385e+27 interpolation 64 -5.67426e-09 3.86437e+27 interpolation 65 -2.73774e-09 3.44055e+28 bisection 66 -1.26948e-09 3.45082e+29 bisection 67 -5.35356e-10 4.60127e+30 bisection 68 1.98773e-10 -8.98945e+31 bisection 69 -1.68291e-10 1.48122e+32 interpolation 70 -1.58322e-10 1.77902e+32 interpolation 71 6.01394e-11 -3.24584e+33 bisection 72 -4.90913e-11 5.96748e+33 interpolation 73 -4.34968e-11 8.5789e+33 interpolation 74 2.16576e-11 -6.94987e+34 bisection 75 1.79564e-11 -1.2194e+35 interpolation 76 -1.09196e-11 5.42225e+35 bisection 77 -1.04523e-11 6.18255e+35 interpolation 78 3.51839e-12 -1.62096e+37 bisection 79 -3.46696e-12 1.69417e+37 interpolation 80 -3.46652e-12 1.69482e+37 interpolation 81 -1.68184e-12 1.48407e+38 bisection 82 -7.89496e-13 1.43468e+39 bisection 83 -3.43326e-13 1.74456e+40 bisection 84 -1.2024e-13 4.06118e+41 bisection 85 1.02845e-13 -6.49023e+41 bisection 86 1.02401e-13 -6.57504e+41 interpolation 87 4.68513e-14 -6.86499e+42 bisection 88 1.90767e-14 -1.01694e+44 bisection 89 -8.69793e-15 1.0729e+45 bisection 90 -6.26527e-15 2.87068e+45 interpolation 91 5.18938e-15 -5.05194e+45 bisection 92 4.74529e-15 -6.60718e+45 interpolation 93 2.10367e-15 -7.58352e+46 bisection 94 7.82863e-16 -1.47146e+48 bisection 95 -5.37947e-16 4.5351e+48 bisection Current point x may be near a singular point. The interval [-0.07, 0.476274] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 4.535e+48 x -0.000 Search for an interval around 0.275 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.275 -24277 0.275 -24277 initial interval 3 0.267222 -26773.1 0.282778 -22062.3 search 5 0.264 -27899.7 0.286 -21218.2 search 7 0.259444 -29595.4 0.290556 -20091.1 search 9 0.253 -32218.6 0.297 -18619.7 search 11 0.243887 -36444.3 0.306113 -16756.7 search 13 0.231 -43681 0.319 -14493.4 search 15 0.212775 -57314.2 0.337225 -11889.1 search 17 0.187 -87358.1 0.363 -9095.75 search 19 0.150549 -175253 0.399451 -6352.26 search 21 0.099 -654748 0.451 -3931.67 search 23 0.0260984 -3.86703e+07 0.523902 -2049.76 search 24 -0.077 1.66688e+06 0.523902 -2049.76 search Search for a zero in the interval [-0.077, 0.523902]: Func-count x f(x) Procedure 24 0.523902 -2049.76 initial 25 0.523164 -2063.26 interpolation 26 0.223082 -49035.9 bisection 27 -0.077 1.66688e+06 bisection 28 0.0730409 -1.67813e+06 interpolation 29 0.0730389 -1.67827e+06 interpolation 30 0.0354035 -1.53417e+07 bisection 31 0.0165858 -1.52148e+08 bisection 32 0.007177 -1.89593e+09 bisection 33 0.00247258 -4.65877e+10 bisection 34 -0.00223185 6.36486e+10 bisection 35 -0.00223148 6.36802e+10 interpolation 36 -0.00105556 6.0093e+11 bisection 37 -0.000467595 6.90877e+12 bisection 38 -0.000173615 1.34934e+14 bisection 39 0.000120366 -4.04805e+14 bisection 40 0.000118792 -4.21106e+14 interpolation 41 4.60837e-05 -7.21344e+15 bisection 42 -2.66245e-05 3.74085e+16 bisection 43 -2.49329e-05 4.5551e+16 interpolation 44 9.72958e-06 -7.66511e+17 bisection 45 -7.60166e-06 1.60725e+18 interpolation 46 -5.97661e-06 3.30707e+18 interpolation 47 4.13315e-06 -9.99904e+18 bisection 48 4.07771e-06 -1.04125e+19 interpolation 49 1.57799e-06 -1.79677e+20 bisection 50 -9.21728e-07 9.01564e+20 bisection 51 -8.67774e-07 1.0804e+21 interpolation 52 3.2813e-07 -1.99832e+22 bisection 53 -2.69822e-07 3.59396e+22 interpolation 54 -2.42567e-07 4.94662e+22 interpolation 55 1.14461e-07 -4.708e+23 bisection 56 8.78412e-08 -1.04162e+24 interpolation 57 -6.40533e-08 2.68646e+24 bisection 58 -6.35701e-08 2.74818e+24 interpolation 59 -2.58381e-08 4.09284e+25 bisection 60 1.1894e-08 -4.19588e+26 bisection 61 8.73108e-09 -1.06072e+27 interpolation 62 -6.97205e-09 2.08317e+27 bisection 63 -6.95632e-09 2.09733e+27 interpolation 64 -3.0384e-09 2.51692e+28 bisection 65 -1.07944e-09 5.61312e+29 bisection 66 8.79514e-10 -1.03771e+30 bisection 67 8.78078e-10 -1.04281e+30 interpolation 68 3.89056e-10 -1.19886e+31 bisection 69 1.44546e-10 -2.33771e+32 bisection 70 -9.99651e-11 7.0674e+32 bisection 71 -9.86246e-11 7.35952e+32 interpolation 72 -3.81672e-11 1.2698e+34 bisection 73 2.22902e-11 -6.3747e+34 bisection 74 2.09838e-11 -7.64105e+34 interpolation 75 -7.93845e-12 1.41123e+36 bisection 76 6.52267e-12 -2.54407e+36 interpolation 77 5.85509e-12 -3.51726e+36 interpolation 78 -2.77881e-12 3.29026e+37 bisection 79 -2.15284e-12 7.07572e+37 interpolation 80 1.53814e-12 -1.94007e+38 bisection 81 1.52353e-12 -1.99641e+38 interpolation 82 6.08091e-13 -3.13977e+39 bisection 83 -3.07349e-13 2.43169e+40 bisection 84 -2.59365e-13 4.04643e+40 interpolation 85 1.50371e-13 -2.0764e+41 bisection 86 1.41062e-13 -2.5152e+41 interpolation 87 -5.44968e-14 4.36206e+42 bisection 88 4.32827e-14 -8.70685e+42 interpolation 89 3.58478e-14 -1.53256e+43 interpolation 90 -2.18605e-14 6.75807e+43 bisection 91 -2.09457e-14 7.68282e+43 interpolation 92 6.99363e-15 -2.06394e+45 bisection 93 -6.97603e-15 2.0796e+45 interpolation 94 -6.53194e-15 2.53325e+45 interpolation 95 -3.24837e-15 2.05972e+46 bisection 96 -1.60658e-15 1.70253e+47 bisection 97 -7.85692e-16 1.45562e+48 bisection Current point x may be near a singular point. The interval [-0.077, 0.523902] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 1.456e+48 x -0.000 Search for an interval around 0.3 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.3 -17979.7 0.3 -17979.7 initial interval 3 0.291515 -19863.5 0.308485 -16309.5 search 5 0.288 -20714.1 0.312 -15673.2 search 7 0.283029 -21995 0.316971 -14824 search 9 0.276 -23977.4 0.324 -13715.9 search 11 0.266059 -27173.1 0.333941 -12314 search 13 0.252 -32651.3 0.348 -10612.7 search 15 0.232118 -42985.7 0.367882 -8658.11 search 17 0.204 -65803.2 0.396 -6566.38 search 19 0.164235 -132732 0.435765 -4518.88 search 21 0.108 -499181 0.492 -2721.51 search 23 0.028471 -2.97128e+07 0.571529 -1335.16 search 24 -0.084 1.29241e+06 0.571529 -1335.16 search Search for a zero in the interval [-0.084, 0.571529]: Func-count x f(x) Procedure 24 0.571529 -1335.16 initial 25 0.570852 -1343.46 interpolation 26 0.243426 -36676.1 bisection 27 0.0797131 -1.28159e+06 bisection 28 0.0797131 -1.28159e+06 bisection 29 0.0797117 -1.28167e+06 interpolation 30 0.0387841 -1.16281e+07 bisection 31 0.0183203 -1.12695e+08 bisection 32 0.00808845 -1.32328e+09 bisection 33 0.00297251 -2.67999e+10 bisection 34 -0.00214344 7.18471e+10 bisection 35 -0.00212502 7.373e+10 interpolation 36 -0.000855244 1.12956e+12 bisection 37 0.000414533 -9.90706e+12 bisection 38 0.000331668 -1.93441e+13 interpolation 39 -0.000220355 6.59979e+13 bisection 40 -0.000215977 7.0093e+13 interpolation 41 -8.01605e-05 1.37075e+15 bisection 42 5.56563e-05 -4.09483e+15 bisection 43 5.49396e-05 -4.2572e+15 interpolation 44 2.13438e-05 -7.26078e+16 bisection 45 -1.22521e-05 3.83866e+17 bisection 46 -1.14358e-05 4.72073e+17 interpolation 47 4.54583e-06 -7.51557e+18 bisection 48 -3.44499e-06 1.72681e+19 interpolation 49 -2.3895e-06 5.17469e+19 interpolation 50 2.12264e-06 -7.38201e+19 bisection 51 2.12208e-06 -7.38785e+19 interpolation 52 9.94325e-07 -7.18156e+20 bisection 53 4.30448e-07 -8.85203e+21 bisection 54 1.48509e-07 -2.15549e+23 bisection 55 -1.3343e-07 2.97199e+23 bisection 56 -1.33404e-07 2.97369e+23 interpolation 57 -6.29323e-08 2.83259e+24 bisection 58 -2.76963e-08 3.32306e+25 bisection 59 -1.00783e-08 6.89666e+26 bisection 60 7.53966e-09 -1.64721e+27 bisection 61 7.49783e-09 -1.67494e+27 interpolation 62 3.11425e-09 -2.33747e+28 bisection 63 -1.26934e-09 3.45203e+29 bisection 64 9.22455e-10 -8.99435e+29 interpolation 65 -6.61437e-10 2.43971e+30 interpolation 66 4.95817e-10 -5.79217e+30 bisection 67 4.93133e-10 -5.88724e+30 interpolation 68 2.05162e-10 -8.17555e+31 bisection 69 -8.28103e-11 1.24323e+33 bisection 70 6.11756e-11 -3.08368e+33 interpolation 71 -4.14395e-11 9.92112e+33 interpolation 72 3.68436e-11 -1.41162e+34 bisection 73 3.68342e-11 -1.41271e+34 interpolation 74 1.72681e-11 -1.3711e+35 bisection 75 7.48509e-12 -1.6835e+36 bisection 76 2.59357e-12 -4.04677e+37 bisection 77 -2.29794e-12 5.81823e+37 bisection 78 -2.29729e-12 5.82317e+37 interpolation 79 -1.07473e-12 5.68725e+38 bisection 80 -4.63457e-13 7.09212e+39 bisection 81 -1.57819e-13 1.79609e+41 bisection 82 1.47819e-13 -2.18581e+41 bisection 83 1.47375e-13 -2.20563e+41 interpolation 84 7.11876e-14 -1.95701e+42 bisection 85 3.30938e-14 -1.94788e+43 bisection 86 1.4047e-14 -2.54716e+44 bisection 87 -4.9999e-15 5.64833e+45 bisection 88 4.52353e-15 -7.62731e+45 interpolation 89 4.07944e-15 -1.03992e+46 interpolation 90 1.56572e-15 -1.83934e+47 bisection 91 -9.48004e-16 8.28656e+47 bisection 92 -5.03915e-16 5.51739e+48 interpolation Current point x may be near a singular point. The interval [-0.084, 0.571529] reduced to the requested tolerance and the function changes sign in the interval, but f(x) increased in magnitude as the interval reduced. exitflag -5 residual 5.517e+48 x -0.000 Search for an interval around 0.325 containing a sign change: Func-count a f(a) b f(b) Procedure 1 0.325 -13566.5 0.325 -13566.5 initial interval 3 0.315808 -15017.6 0.334192 -12280.9 search 5 0.312 -15673.2 0.338 -11791.4 search 7 0.306615 -16660.8 0.343385 -11138.4 search 9 0.299 -18190 0.351 -10286.7 search 11 0.28823 -20657 0.36177 -9210.1 search 13 0.273 -24890.3 0.377 -7904.96 search 15 0.251461 -32887.6 0.398539 -6408.04 search 17 0.221 -50579.4 0.429 -4809.91 search 19 0.177922 -102613 0.472078 -3251.14 search 21 0.117 -388567 0.533 -1890.21 search 23 0.0308436 -2.33123e+07 0.619156 -849.498 search 24 -0.091 1.0232e+06 0.619156 -849.498 search Search for a zero in the interval [-0.091, 0.619156]: Func-count x f(x) Procedure 24 0.619156 -849.498 initial 25 0.618567 -854.474 interpolation 26 0.263784 -27977.4 bisection 27 0.0863918 -999326 bisection 28 0.0863918 -999326 bisection 29 0.0863903 -999381 interpolation 30 0.0420431 -9.09699e+06 bisection 31 0.0198695 -8.81967e+07 bisection 32 0.00878271 -1.03289e+09 bisection 33 0.00323931 -2.07026e+10 bisection 34 -0.00230409 5.78517e+10 bisection 35 -0.00228105 5.96212e+10 interpolation 36 -0.000906716 9.47955e+11 bisection 37 0.000467613 -6.90144e+12 bisection 38 0.000403202 -1.07662e+13 interpolation 39 -0.000219551 6.67255e+13 bisection 40 -0.000198318 9.05327e+13 interpolation 41 9.1825e-05 -9.11761e+14 bisection 42 ...
function hw7
fun = @(e) hw7fun(e);
e0 = 0.05:0.025:1.25;
options = optimset('Display', 'iter');
for k = 1:numel(e0)
[e(k), residual(k), exitflag(k), output(k)] = fzero(fun, e0(k), options);
fprintf('\nexitflag %d residual %6.3e x %6.3f\n', exitflag(k), residual(k), e(k));
end
function f = hw7fun(e)
dp=416;
L=1.5;
h=1e-3;
v=0.1;
d=5e-2;
p=2e3;
f = (dp/L)-150*((h*v)/d^2)*((1-e)^2/e^3)-(7/4)*((p*v^2)/d)*((1-e)/e^3);
% endoutput.funcCount
end
end
.

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