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

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Omorodion Solomon
Omorodion Solomon 2021-7-24
评论： Star Strider 2021-7-31
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)

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Star Strider
Star Strider 2021-7-24
Ran in:
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?
.
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Omorodion Solomon
Omorodion Solomon 2021-7-31
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!

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