Please someone help test run this Matlab code and debug it if possible. Please help a student

alpha=input('simulation time alpha=') [x,t] = meshgrid(-4:.1:4, 0.1:.2:0.4); exact=(sech(x/4-t/4)).^2 f0=(sech(x/4)).^2 f1=1/2.*(sech(x/4)).^2.*tanh(x/4)+1/2.*(sech(x/4)).^4.*tanh(x/4) f2=7/8.*(sech(x/4)).^6.*(tanh(x/4)).^2-1/8.*(sech(x/4)).^6 +5/4.*(sech(x/4)).^4.*(tanh(x/4)).^2-1/4.*(sech(x/4)).^4 +3/8.*(sech(x/4)).^2.*(tanh(x/4)).^2-1/8.*(sech(x/4)).^2 f3=35/16.*(sech(x/4)).^8.*(tanh(x/4)).^3-11/6.*(sech(x/4)).^8.*tanh(x/4) +17/4.*(sech(x/4)).^6.*(tanh(x/4)).^3-13/8.*((sech(x/4))).^6.*tanh(x/4) +39/16.*(sech(x/4)).^4.*(tanh(x/4)).^3-19/16.*(sech(x/4)).^4.*tanh(x/4) +3/8.*(sech(x/4)).^2.*((tanh(x/4)).^3)-1/4.*(sech(x/4)).^2.*tanh(x/4) f4=385/64.*(sech(x/4)).^8.*(tanh(x/4)).^4-35/16.*sech(x/4).*tanh(x/4)-51/16 .*(sech(x/4)).^8.*(tanh(x/4)).^2+153/16.*(sech(x/4)).^6.*(tanh(x/4)).^4 +11/16.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^8.*tanh(x/4) .*(-1/2.*(sech(x/4)).^2.*tanh(x/4))-17/4.*sech(x/4).*(-1/2.*(sech(x/4)).^2 .*tanh(x/4)).^6.*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^3+11/64 .*(sech(x/4)).^8-193/32.*(sech(x/4)).^6.*(tanh(x/4)).^2+273/64 .*(sech(x/4)).^4.*(tanh(x/4)).^4+13/8.*sech(x/4).*(-1/2*(sech(x/4)).^2).^6 .*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4))-39/16.*sech(x/4) .*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^7.*tanh(x/4)+13/32.*(sech(x/4)).^6 -53/16.*(sech(x/4)).^4.*(tanh(x/4)).^2+15/32.*(sech(x/4)).^2 .*(tanh(x/4)).^4+19/16.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^5 .*tanh(x/4)-3/8.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^5.*tanh(x/4) +19/64.*(sech(x/4)).^4-15/32.*(sech(x/4)).^2.*(tanh(x/4)).^2+1/4.*sech(x/4) .*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^3-sech(x/4)-35/8 .*(sech(x/4)).^8.*(tanh(x/4)).^4+105/16.*(sech(x/4)).^8.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+11/8.*(sech(x/4)).^8.*(tanh(x/4)).^4-11/16 .*(sech(x/4)).^.8.*(1/4-1/4.*(tanh(x/4)).^2)-51/.8.*(sech(x/4)).^.6 .*(tanh(x/4)).^4+51/4.*(sech(x/4)).^6.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+39/16.*(sech(x/4)).^6.*(tanh(x/4)).^2 -13/8 .*(sech(x/4)).^6.*(1/4-1/4.*(tanh(x/4)).^2)-39/16.*(sech(x/4)).^4 .*(tanh(x/4)).^4+117/16.*(sech(x/4)).^4.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+19/16.*(sech(x/4)).^4.*(tanh(x/4)).^2-19/16 .*(sech(x/4)).^4.*(1/4-1/4.*(tanh(x/4)).^2)-3/16.*(sech(x/4)).^2 .*(tanh(x/4)).^4+9/8.*(sech(x/4)).^2.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+1/8.*(sech(x/4)).^2.*(tanh(x/4)).^2-1/4 .*(sech(x/4)).^2.*(1/4-1/4.*(tanh(x/4)).^2).^2+1/16.*(sech(x/4)).^2 u4=f0+f1.*((t.^alpha)/gamma(1+alpha))+f2.*((t.^(2.*alpha))/gamma(1+2.*alpha ))+f3.*((t.^(3.*alpha))/gamma(1+3.*alpha))+f4.*((t.^(4.*alpha))/gamma(1+4.* alpha)) Z1=uexact mesh(t,x,Z1) Z2=u4 mesh(t,x,Z2)

[Yongjian Feng]

If you can format it better, others might be able to understand what it is.

[Omorodion Solomon]

Please just copy and paste it on matlab; i copied it my mobile phone.

Answer 1

[Star Strider]

The ‘uexact’ variable does not exist, and there is nothing similar to it (for example by a different spelling, at least that I can see) in the code. Substituting ‘exact’ for it (that does exist) produces a mesh plot.

Otherwise, ‘uexact’ will need to be created for the code to work, since that appears to be the only probllem. (The input call does not work in the onlilne Run feature, so I assigned the ‘alpha’ value separately. I have no idea what it should be , so change it if the value I chose is not appropriate.)

% alpha=input('simulation time alpha=') 
alpha = 100;
[x,t] = meshgrid(-4:.1:4, 0.1:.2:0.4); 
exact=(sech(x/4-t/4)).^2 

exact = 2×81

0.4042 0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.3738 0.3888 0.4042 0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869

f0=(sech(x/4)).^2 

f0 = 2×81

0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280 0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280

f1=1/2.*(sech(x/4)).^2.*tanh(x/4)+1/2.*(sech(x/4)).^4.*tanh(x/4) 

f1 = 2×81

-0.2271 -0.2352 -0.2433 -0.2513 -0.2593 -0.2672 -0.2748 -0.2823 -0.2894 -0.2962 -0.3025 -0.3083 -0.3136 -0.3181 -0.3220 -0.3250 -0.3270 -0.3281 -0.3281 -0.3270 -0.3246 -0.3210 -0.3159 -0.3095 -0.3016 -0.2923 -0.2814 -0.2691 -0.2553 -0.2400 -0.2271 -0.2352 -0.2433 -0.2513 -0.2593 -0.2672 -0.2748 -0.2823 -0.2894 -0.2962 -0.3025 -0.3083 -0.3136 -0.3181 -0.3220 -0.3250 -0.3270 -0.3281 -0.3281 -0.3270 -0.3246 -0.3210 -0.3159 -0.3095 -0.3016 -0.2923 -0.2814 -0.2691 -0.2553 -0.2400

f2=7/8.*(sech(x/4)).^6.*(tanh(x/4)).^2-1/8.*(sech(x/4)).^6 +5/4.*(sech(x/4)).^4.*(tanh(x/4)).^2-1/4.*(sech(x/4)).^4 +3/8.*(sech(x/4)).^2.*(tanh(x/4)).^2-1/8.*(sech(x/4)).^2 

f2 = 2×81

0.1510 0.1548 0.1581 0.1609 0.1630 0.1643 0.1647 0.1641 0.1623 0.1591 0.1546 0.1484 0.1406 0.1309 0.1193 0.1056 0.0899 0.0720 0.0519 0.0296 0.0052 -0.0211 -0.0494 -0.0793 -0.1107 -0.1433 -0.1767 -0.2107 -0.2447 -0.2784 0.1510 0.1548 0.1581 0.1609 0.1630 0.1643 0.1647 0.1641 0.1623 0.1591 0.1546 0.1484 0.1406 0.1309 0.1193 0.1056 0.0899 0.0720 0.0519 0.0296 0.0052 -0.0211 -0.0494 -0.0793 -0.1107 -0.1433 -0.1767 -0.2107 -0.2447 -0.2784

f3=35/16.*(sech(x/4)).^8.*(tanh(x/4)).^3-11/6.*(sech(x/4)).^8.*tanh(x/4) +17/4.*(sech(x/4)).^6.*(tanh(x/4)).^3-13/8.*((sech(x/4))).^6.*tanh(x/4) +39/16.*(sech(x/4)).^4.*(tanh(x/4)).^3-19/16.*(sech(x/4)).^4.*tanh(x/4) +3/8.*(sech(x/4)).^2.*((tanh(x/4)).^3)-1/4.*(sech(x/4)).^2.*tanh(x/4) 

f3 = 2×81

-0.0540 -0.0458 -0.0356 -0.0230 -0.0080 0.0099 0.0307 0.0548 0.0823 0.1133 0.1480 0.1864 0.2284 0.2740 0.3228 0.3746 0.4288 0.4847 0.5418 0.5989 0.6552 0.7093 0.7600 0.8060 0.8459 0.8782 0.9015 0.9146 0.9163 0.9057 -0.0540 -0.0458 -0.0356 -0.0230 -0.0080 0.0099 0.0307 0.0548 0.0823 0.1133 0.1480 0.1864 0.2284 0.2740 0.3228 0.3746 0.4288 0.4847 0.5418 0.5989 0.6552 0.7093 0.7600 0.8060 0.8459 0.8782 0.9015 0.9146 0.9163 0.9057

f4=385/64.*(sech(x/4)).^8.*(tanh(x/4)).^4-35/16.*sech(x/4).*tanh(x/4)-51/16 .*(sech(x/4)).^8.*(tanh(x/4)).^2+153/16.*(sech(x/4)).^6.*(tanh(x/4)).^4 +11/16.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^8.*tanh(x/4) .*(-1/2.*(sech(x/4)).^2.*tanh(x/4))-17/4.*sech(x/4).*(-1/2.*(sech(x/4)).^2 .*tanh(x/4)).^6.*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^3+11/64 .*(sech(x/4)).^8-193/32.*(sech(x/4)).^6.*(tanh(x/4)).^2+273/64 .*(sech(x/4)).^4.*(tanh(x/4)).^4+13/8.*sech(x/4).*(-1/2*(sech(x/4)).^2).^6 .*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4))-39/16.*sech(x/4) .*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^7.*tanh(x/4)+13/32.*(sech(x/4)).^6 -53/16.*(sech(x/4)).^4.*(tanh(x/4)).^2+15/32.*(sech(x/4)).^2 .*(tanh(x/4)).^4+19/16.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^5 .*tanh(x/4)-3/8.*sech(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^5.*tanh(x/4) +19/64.*(sech(x/4)).^4-15/32.*(sech(x/4)).^2.*(tanh(x/4)).^2+1/4.*sech(x/4) .*tanh(x/4).*(-1/2.*(sech(x/4)).^2.*tanh(x/4)).^3-sech(x/4)-35/8 .*(sech(x/4)).^8.*(tanh(x/4)).^4+105/16.*(sech(x/4)).^8.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+11/8.*(sech(x/4)).^8.*(tanh(x/4)).^4-11/16 .*(sech(x/4)).^.8.*(1/4-1/4.*(tanh(x/4)).^2)-51/.8.*(sech(x/4)).^.6 .*(tanh(x/4)).^4+51/4.*(sech(x/4)).^6.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+39/16.*(sech(x/4)).^6.*(tanh(x/4)).^2 -13/8 .*(sech(x/4)).^6.*(1/4-1/4.*(tanh(x/4)).^2)-39/16.*(sech(x/4)).^4 .*(tanh(x/4)).^4+117/16.*(sech(x/4)).^4.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+19/16.*(sech(x/4)).^4.*(tanh(x/4)).^2-19/16 .*(sech(x/4)).^4.*(1/4-1/4.*(tanh(x/4)).^2)-3/16.*(sech(x/4)).^2 .*(tanh(x/4)).^4+9/8.*(sech(x/4)).^2.*(tanh(x/4)).^2 .*(1/4-1/4.*(tanh(x/4)).^2)+1/8.*(sech(x/4)).^2.*(tanh(x/4)).^2-1/4 .*(sech(x/4)).^2.*(1/4-1/4.*(tanh(x/4)).^2).^2+1/16.*(sech(x/4)).^2 

f4 = 2×81

-15.9920 -15.2619 -14.5177 -13.7624 -12.9993 -12.2319 -11.4636 -10.6984 -9.9399 -9.1921 -8.4589 -7.7443 -7.0518 -6.3853 -5.7479 -5.1429 -4.5729 -4.0403 -3.5470 -3.0945 -2.6836 -2.3147 -1.9877 -1.7019 -1.4562 -1.2490 -1.0781 -0.9412 -0.8356 -0.7584 -15.9920 -15.2619 -14.5177 -13.7624 -12.9993 -12.2319 -11.4636 -10.6984 -9.9399 -9.1921 -8.4589 -7.7443 -7.0518 -6.3853 -5.7479 -5.1429 -4.5729 -4.0403 -3.5470 -3.0945 -2.6836 -2.3147 -1.9877 -1.7019 -1.4562 -1.2490 -1.0781 -0.9412 -0.8356 -0.7584

u4=f0+f1.*((t.^alpha)/gamma(1+alpha))+f2.*((t.^(2.*alpha))/gamma(1+2.*alpha ))+f3.*((t.^(3.*alpha))/gamma(1+3.*alpha))+f4.*((t.^(4.*alpha))/gamma(1+4.* alpha)) 

u4 = 2×81

0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280 0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280

% Z1=uexact 
Z1 = exact;

figure
mesh(t,x,Z1)
xlabel('t')
ylabel('x')
zlabel('Z_1')

Z2=u4 

Z2 = 2×81

0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280 0.4200 0.4362 0.4527 0.4696 0.4869 0.5045 0.5224 0.5406 0.5591 0.5777 0.5966 0.6156 0.6347 0.6540 0.6732 0.6924 0.7116 0.7306 0.7495 0.7681 0.7864 0.8044 0.8220 0.8391 0.8556 0.8716 0.8869 0.9014 0.9151 0.9280

figure
mesh(t,x,Z2)
xlabel('t')
ylabel('x')
zlabel('Z_2')

Is this the desired result?

.

[Omorodion Solomon]

Oh my God…Thank you soooo much sir. This is the desired result.

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

[Omorodion Solomon]

Please I want to plot the graph of the exact solution and approximate solution in a single graph for t=0.44 and alpha=1.

[Omorodion Solomon]

See sample

[Star Strider]

I saw both of those and solved them.

The proper expression of appreciation here on MATLAB Answer is to Accept an Answer that best solves the posted problem.

.

[Omorodion Solomon]

I'm new to this environment. I've accepted your answer. Please kindly assist to plot the graph of the exact solution and approximate solution in a single graph. Kind regards!

[Star Strider]

Thank you!

I completely udnerstand.

.