can anyone help me show the result

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Relly Syam
Relly Syam on 9 Jun 2021
Commented: Walter Roberson on 9 Jun 2021
%clear;
clc;
format long e
tic
%bagian n=10
syms c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 t r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
c0=0; c1=1/10; c2=2/10; c3=3/10; c4=4/10; c5=5/10; c6=6/10; c7=7/10; c8=8/10; c9=9/10; c10=10/10; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6; r7=7; r8=8; r9=9; r10=10;
EvalAt = [c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10],t),t,0,EA).', EvalAt, 'uniform', 0);
E = horzcat(ktemp{:}).'
K = horzcat(ptemp{:}).'
Ek=E-K
Inv_Ek= inv(Ek) ;
F=[1-c0*(sin(c0)-cos(c0));1-c1*(sin(c1)-cos(c1));1-c2*(sin(c2)-cos(c2));1-c3*(sin(c3)-cos(c3));1-c4*(sin(c4)-cos(c4));1-c5*(sin(c5)-cos(c5));1-c6*(sin(c6)-cos(c6));1-c7*(sin(c7)-cos(c7));1-c8*(sin(c8)-cos(c8));1-c9*(sin(c9)-cos(c9));1-c10*(sin(c10)-cos(c10))]
C=Ek\F
%solusi aproximasinya
Ua=@(x)(C(1)*euler(0,x)+C(2)*euler(1,x)+C(3)*euler(2,x)+C(4)*euler(3,x)+C(5)*euler(4,x)+C(6)*euler(5,x)+C(7)*euler(6,x)+C(8)*euler(7,x)+C(9)*euler(8,x)+C(10)*euler(9,x)+C(11)*euler(10,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa(i)=Ua(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap= uaa;
Uex= uee;
y=(abs(uaa-uee));
[xx uee uaa y];
uee
uaa
y
%bagian n=6
syms s0 s1 s2 s3 s4 s5 s6 t r0 r1 r2 r3 r4 r5 r6
s0=0/6; s1=1/6; s2=2/6; s3=3/6; s4=4/6; s5=5/6; s6=6/6; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6;
EvalAt = [s0, s1, s2, s3, s4, s5, s6];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6],t),t,0,EA).', EvalAt, 'uniform', 0);
E2 = horzcat(ktemp{:}).'
K2 = horzcat(ptemp{:}).'
Ek2=E2-K2
Inv_Ek2= inv(Ek2) ;
F2=[1-s0*(sin(s0)-cos(s0));1-s1*(sin(s1)-cos(s1));1-s2*(sin(s2)-cos(s2));1-s3*(sin(s3)-cos(s3));1-s4*(sin(s4)-cos(s4));1-s5*(sin(s5)-cos(s5));1-s6*(sin(s6)-cos(s6))]
C2=Ek2\F2
%solusi aproximasinya
Ua2=@(x)(C2(1)*euler(0,x)+C2(2)*euler(1,x)+C2(3)*euler(2,x)+C2(4)*euler(3,x)+C2(5)*euler(4,x)+C2(6)*euler(5,x)+C2(7)*euler(6,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa2=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa2(i)=Ua2(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap2= uaa2;
Uex= uee;
y2=(abs(uaa2-uee));
[xx uee uaa2 y2];
uee
uaa2
y2
%bagian n=2
syms w0 w1 w2 t r0 r1 r2
w0=0/2; w1=1/2; w2=2/2; r0=0; r1=1; r2=2;
EvalAt = [w0, w1, w2];
ktemp = arrayfun(@(EA) euler([r0, r1, r2], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2],t),t,0,EA).', EvalAt, 'uniform', 0);
E3 = horzcat(ktemp{:}).'
K3 = horzcat(ptemp{:}).'
Ek3=E3-K3
Inv_Ek3= inv(Ek3) ;
F3=[1-w0*(sin(w0)-cos(w0));1-w1*(sin(w1)-cos(w1));1-w2*(sin(w2)-cos(w2))]
C3=Ek3\F3
%solusi aproximasinya
Ua3=@(x)(C3(1)*euler(0,x)+C3(2)*euler(1,x)+C3(3)*euler(2,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa3=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa3(i)=Ua3(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap3= uaa3;
Uex= uee;
y3=(abs(uaa3-uee));
[xx uee uaa3 y3];
uee
uaa3
y3
%gambar
plot(xx,uee,'k',xx,uaa,'o',xx,uaa2,'c*',xx,uaa3,'--')
grid on
legend({'eksak','aproksimasi N=10','aproksimasi N=6','aproksimasi N=2'},'Location','Northwest')
plot(xx,y)
title('Error N=10')
plot(xx,y2)
title('Error N=6')
plot(xx,y3)
title('Error N=2')
grid on
toc
  1 Comment
Walter Roberson
Walter Roberson on 9 Jun 2021
What is the difference between what is displayed now, and what you want to display?
Note: you have very few comments, and you did not post the equations, so we do not know what you want to compute.
%clear;
clc;
format long g
tic
%bagian n=10
syms c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 t r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
c0=0; c1=1/10; c2=2/10; c3=3/10; c4=4/10; c5=5/10; c6=6/10; c7=7/10; c8=8/10; c9=9/10; c10=10/10; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6; r7=7; r8=8; r9=9; r10=10;
EvalAt = [c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10],t),t,0,EA).', EvalAt, 'uniform', 0);
E = horzcat(ktemp{:}).'
E = 11×11
1 -0.5 0 0.25 0 -0.5 0 2.125 0 -15.5 0 1 -0.4 -0.09 0.236 0.0981 -0.47524 -0.295029 2.0208716 1.67213961 -14.741279044 -15.2462570049 1 -0.3 -0.16 0.198 0.1856 -0.40368 -0.560896 1.7187888 3.18043136 -12.539467008 -28.9999384576 1 -0.2 -0.21 0.142 0.2541 -0.29282 -0.771561 1.2485422 4.37721081 -9.110266562 -39.9147115101 1 -0.1 -0.24 0.074 0.2976 -0.15376 -0.906624 0.6563024 5.14546176 -4.789470976 -46.9222938624 1 0 -0.25 0 0.3125 0 -0.953125 0 5.41015625 0 -49.3369140625 1 0.1 -0.24 -0.074 0.2976 0.15376 -0.906624 -0.6563024 5.14546176 4.789470976 -46.9222938624 1 0.2 -0.21 -0.142 0.2541 0.29282 -0.771561 -1.2485422 4.37721081 9.110266562 -39.9147115101 1 0.3 -0.16 -0.198 0.1856 0.40368 -0.560896 -1.7187888 3.18043136 12.539467008 -28.9999384576 1 0.4 -0.09 -0.236 0.0981 0.47524 -0.295029 -2.0208716 1.67213961 14.741279044 -15.2462570049
K = horzcat(ptemp{:}).'
K = 
Ek=E-K
Ek = 
Inv_Ek= inv(Ek) ;
F=[1-c0*(sin(c0)-cos(c0));1-c1*(sin(c1)-cos(c1));1-c2*(sin(c2)-cos(c2));1-c3*(sin(c3)-cos(c3));1-c4*(sin(c4)-cos(c4));1-c5*(sin(c5)-cos(c5));1-c6*(sin(c6)-cos(c6));1-c7*(sin(c7)-cos(c7));1-c8*(sin(c8)-cos(c8));1-c9*(sin(c9)-cos(c9));1-c10*(sin(c10)-cos(c10))]
F = 11×1
1 1.08951707486312 1.15627944940924 1.19794488473928 1.21265706067769 1.19907851164308 1.15641588490879 1.08443715003276 0.983480494758114 0.854454752778863
C=Ek\F
C = 
%solusi aproximasinya
Ua=@(x)(C(1)*euler(0,x)+C(2)*euler(1,x)+C(3)*euler(2,x)+C(4)*euler(3,x)+C(5)*euler(4,x)+C(6)*euler(5,x)+C(7)*euler(6,x)+C(8)*euler(7,x)+C(9)*euler(8,x)+C(10)*euler(9,x)+C(11)*euler(10,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa(i)=Ua(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap= uaa;
Uex= uee;
y=(abs(uaa-uee));
[xx uee uaa y];
uee
uee = 11×1
1 1.09483758192485 1.1787359086363 1.25085669578695 1.31047933631154 1.35700810049458 1.38997808830471 1.40905987452218 1.41406280024669 1.40493687789815
uaa
uaa = 11×1
1 1.09483758192485 1.1787359086363 1.25085669578695 1.31047933631154 1.35700810049458 1.38997808830471 1.40905987452218 1.41406280024669 1.40493687789815
y
y = 11×1
0 2.22044604925031e-16 2.22044604925031e-16 2.22044604925031e-16 0 0 0 2.22044604925031e-16 0 4.44089209850063e-16
%bagian n=6
syms s0 s1 s2 s3 s4 s5 s6 t r0 r1 r2 r3 r4 r5 r6
s0=0/6; s1=1/6; s2=2/6; s3=3/6; s4=4/6; s5=5/6; s6=6/6; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6;
EvalAt = [s0, s1, s2, s3, s4, s5, s6];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6],t),t,0,EA).', EvalAt, 'uniform', 0);
E2 = horzcat(ktemp{:}).'
E2 = 7×7
1 -0.5 0 0.25 0 -0.5 0 1 -0.333333333333333 -0.138888888888889 0.212962962962963 0.158179012345679 -0.432355967078189 -0.47721622085048 1 -0.166666666666667 -0.222222222222222 0.12037037037037 0.271604938271605 -0.248971193415638 -0.825788751714678 1 0 -0.25 0 0.3125 0 -0.953125 1 0.166666666666667 -0.222222222222222 -0.12037037037037 0.271604938271605 0.248971193415638 -0.825788751714678 1 0.333333333333333 -0.138888888888889 -0.212962962962963 0.158179012345679 0.432355967078189 -0.47721622085048 1 0.5 0 -0.25 0 0.5 0
K2 = horzcat(ptemp{:}).'
K2 = 
Ek2=E2-K2
Ek2 = 
Inv_Ek2= inv(Ek2) ;
F2=[1-s0*(sin(s0)-cos(s0));1-s1*(sin(s1)-cos(s1));1-s2*(sin(s2)-cos(s2));1-s3*(sin(s3)-cos(s3));1-s4*(sin(s4)-cos(s4));1-s5*(sin(s5)-cos(s5));1-s6*(sin(s6)-cos(s6))]
F2 = 7×1
1 1.13670784981159 1.20592074983953 1.19907851164308 1.11167830513814 0.94352949240585 0.698831321060243
C2=Ek2\F2
C2 = 
%solusi aproximasinya
Ua2=@(x)(C2(1)*euler(0,x)+C2(2)*euler(1,x)+C2(3)*euler(2,x)+C2(4)*euler(3,x)+C2(5)*euler(4,x)+C2(6)*euler(5,x)+C2(7)*euler(6,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa2=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa2(i)=Ua2(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap2= uaa2;
Uex= uee;
y2=(abs(uaa2-uee));
[xx uee uaa2 y2];
uee
uee = 11×1
1 1.09483758192485 1.1787359086363 1.25085669578695 1.31047933631154 1.35700810049458 1.38997808830471 1.40905987452218 1.41406280024669 1.40493687789815
uaa2
uaa2 = 11×1
1 1.09483760378775 1.17873590315506 1.25085669267594 1.31047933999803 1.35700810070677 1.38997808514249 1.40905987717017 1.41406280490202 1.40493686337285
y2
y2 = 11×1
0 2.18628921633268e-08 5.4812476779631e-09 3.11100167849077e-09 3.68649466508941e-09 2.12197814875026e-10 3.16222048546422e-09 2.64798871718597e-09 4.65532767890409e-09 1.45252985195299e-08
%bagian n=2
syms w0 w1 w2 t r0 r1 r2
w0=0/2; w1=1/2; w2=2/2; r0=0; r1=1; r2=2;
EvalAt = [w0, w1, w2];
ktemp = arrayfun(@(EA) euler([r0, r1, r2], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2],t),t,0,EA).', EvalAt, 'uniform', 0);
E3 = horzcat(ktemp{:}).'
E3 = 3×3
1 -0.5 0 1 0 -0.25 1 0.5 0
K3 = horzcat(ptemp{:}).'
K3 = 
Ek3=E3-K3
Ek3 = 
Inv_Ek3= inv(Ek3) ;
F3=[1-w0*(sin(w0)-cos(w0));1-w1*(sin(w1)-cos(w1));1-w2*(sin(w2)-cos(w2))]
F3 = 3×1
1 1.19907851164308 0.698831321060243
C3=Ek3\F3
C3 = 
%solusi aproximasinya
Ua3=@(x)(C3(1)*euler(0,x)+C3(2)*euler(1,x)+C3(3)*euler(2,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa3=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa3(i)=Ua3(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap3= uaa3;
Uex= uee;
y3=(abs(uaa3-uee));
[xx uee uaa3 y3];
uee
uee = 11×1
1 1.09483758192485 1.1787359086363 1.25085669578695 1.31047933631154 1.35700810049458 1.38997808830471 1.40905987452218 1.41406280024669 1.40493687789815
uaa3
uaa3 = 11×1
1 1.09811501918109 1.18290509767495 1.25437023548158 1.31251043260098 1.35732568903315 1.38881600477809 1.4069813798358 1.41182181420628 1.40333730788953
y3
y3 = 11×1
0 0.00327743725623475 0.00416918903864505 0.00351353969463131 0.00203109628944098 0.000317588538570668 0.00116208352662706 0.00207849468638233 0.00224098604041023 0.00159957000861866
%gambar
plot(xx,uee,'k',xx,uaa,'o',xx,uaa2,'c*',xx,uaa3,'--')
grid on
legend({'eksak','aproksimasi N=10','aproksimasi N=6','aproksimasi N=2'},'Location','Northwest')
plot(xx,y)
title('Error N=10')
plot(xx,y2)
title('Error N=6')
plot(xx,y3)
title('Error N=2')
grid on
toc
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