Please assist! Z1= exact solution; Z2= approximate solution. Now i want to plot a 2D graph of the exact and approximate solution in ONE graph to campare the results

alpha=1;t=0.004; [x,t] = meshgrid(-4:.1:4, 0.1:.2:0.4); exact=(sech(x/4-t/4)).^2; f0=(sech(x/4)).^2; f1=(sinh(x/4).*(cosh(x/4).^2+1))./(2.*cosh(x/4).^5); f2= ((2.*sinh(x/4)+2.*cosh(x/4).^5+sinh(x/4).^3).*(cosh(x/4).^2+2.*cosh(x/4).^4-5))./(16.*cosh(x/4).^11); f3= (486.*cosh(x/4).^4.*sinh(x/4)-150.*cosh(x/4).^2.*sinh(x/4)-275.*sinh(x/4)+240.*cosh(x/4).^6.*sinh(x/4)-259.*cosh(x/4).^8.*sinh(x/4)+486.*cosh(x/4).^10.*sinh(x/4)-160.*cosh(x/4).^12.*sinh(x/4)-288.*cosh(x/4).^14.*sinh(x/4)-912.*cosh(x/4).^16.*sinh(x/4)+160.*cosh(x/4).^18.*sinh(x/4)+ 128.*cosh(x/4).^20.*sinh(x/4)-850.*cosh(x/4).^5+ 350.*cosh(x/4).^7+1174.*cosh(x/4).^9+514.*cosh(x/4).^1 -668.*cosh(x/4).^13-776.*cosh(x/4).^15+176.*cosh(x/4).^17+128.*cosh(x/4).^19)./(1024.*cosh(x/4).^23); f4=(6873300.*cosh(x/4).^4.*sinh(x/4)-151250.*cosh(x/4).^2.*sinh(x/4)-1739375.*sinh(x/4)+ 660000.*cosh(x/4).^6.*sinh(x/4)-11104474.*cosh(x/4).^8.*sinh(x/4)[phone].*cosh(x/4).^10.*sinh(x/4)-5089324.*cosh(x/4).^12.*sinh(x/4)-42875520.*cosh(x/4).^14.*sinh(x/4)-3455535.*cosh(x/4).^16.*sinh(x/4)+ 56411614.*cosh(x/4).^18.*sinh(x/4)[phone].*cosh(x/4).^20.*sinh(x/4)-31724640.*cosh(x/4).^22.*sinh(x/4)- 36843664.*cosh(x/4).^24.*sinh(x/4)+ 13863840.*cosh(x/4).^26.*sinh(x/4)-13521024.*cosh(x/4).^28.*sinh(x/4)+8647168.*cosh(x/4).^30.*sinh(x/4) [phone].*cosh(x/4).^32.*sinh(x/4)[phone].*cosh(x/4).^34.*sinh(x/4)- 7403520.*cosh(x/4).^36.*sinh(x/4)-7286784.*cosh(x/4).^38.*sinh(x/4)+1155072.*cosh(x/4).^40.*sinh(x/4)+ 557056.*cosh(x/4).^42.*sinh(x/4)-9583750.*cosh(x/4).^5+8131250*cosh(x/4).^7+30360150.*cosh(x/4).^9-16086950.*cosh(x/4).^11-44329262.*cosh(x/4).^13+20818214.*cosh(x/4).^15+14048786.*cosh(x/4).^17-4409026.*cosh(x/4).^19-19030068*cosh(x/4).^21+46003792.*cosh(x/4).^23+10034944.*cosh(x/4).^25- 46183616.*cosh(x/4).^27-11517056.*cosh(x/4).^29+16566784.*cosh(x/4).^31+3445248.*cosh(x/4).^33+ 4956672.*cosh(x/4).^35-1250304.*cosh(x/4).^37+4407296.*cosh(x/4).^39-6324224.*cosh(x/4).^41+ 262144.*cosh(x/4).^43+262144.*cosh(x/4).^45)./(4194304.*cosh(x/4).^47); 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=exact;Z2=u4; plot(t,x,Z1) xlabel('x') ylabel('u')

[Star Strider]

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

.

Answer 1

[Star Strider]

Try this:

alpha=1;
t=0.004; 
[x,t] = meshgrid(-4:.1:4, 0.1:.2:0.4); 
exact=(sech(x/4-t/4)).^2; 
f0=(sech(x/4)).^2; 
f1=(sinh(x/4).*(cosh(x/4).^2+1))./(2.*cosh(x/4).^5); 
f2= ((2.*sinh(x/4)+2.*cosh(x/4).^5+sinh(x/4).^3).*(cosh(x/4).^2+2.*cosh(x/4).^4-5))./(16.*cosh(x/4).^11); 
f3= (486.*cosh(x/4).^4.*sinh(x/4)-150.*cosh(x/4).^2.*sinh(x/4)-275.*sinh(x/4)+240.*cosh(x/4).^6.*sinh(x/4)-259.*cosh(x/4).^8.*sinh(x/4)+486.*cosh(x/4).^10.*sinh(x/4)-160.*cosh(x/4).^12.*sinh(x/4)-288.*cosh(x/4).^14.*sinh(x/4)-912.*cosh(x/4).^16.*sinh(x/4)+160.*cosh(x/4).^18.*sinh(x/4)+ 128.*cosh(x/4).^20.*sinh(x/4)-850.*cosh(x/4).^5+ 350.*cosh(x/4).^7+1174.*cosh(x/4).^9+514.*cosh(x/4).^1 -668.*cosh(x/4).^13-776.*cosh(x/4).^15+176.*cosh(x/4).^17+128.*cosh(x/4).^19)./(1024.*cosh(x/4).^23); 
f4=(6873300.*cosh(x/4).^4.*sinh(x/4)-151250.*cosh(x/4).^2.*sinh(x/4)-1739375.*sinh(x/4)+ 660000.*cosh(x/4).^6.*sinh(x/4)-11104474.*cosh(x/4).^8.*sinh(x/4)[phone].*cosh(x/4).^10.*sinh(x/4)-5089324.*cosh(x/4).^12.*sinh(x/4)-42875520.*cosh(x/4).^14.*sinh(x/4)-3455535.*cosh(x/4).^16.*sinh(x/4)+ 56411614.*cosh(x/4).^18.*sinh(x/4)[phone].*cosh(x/4).^20.*sinh(x/4)-31724640.*cosh(x/4).^22.*sinh(x/4)- 36843664.*cosh(x/4).^24.*sinh(x/4)+ 13863840.*cosh(x/4).^26.*sinh(x/4)-13521024.*cosh(x/4).^28.*sinh(x/4)+8647168.*cosh(x/4).^30.*sinh(x/4) [phone].*cosh(x/4).^32.*sinh(x/4)[phone].*cosh(x/4).^34.*sinh(x/4)- 7403520.*cosh(x/4).^36.*sinh(x/4)-7286784.*cosh(x/4).^38.*sinh(x/4)+1155072.*cosh(x/4).^40.*sinh(x/4)+ 557056.*cosh(x/4).^42.*sinh(x/4)-9583750.*cosh(x/4).^5+8131250*cosh(x/4).^7+30360150.*cosh(x/4).^9-16086950.*cosh(x/4).^11-44329262.*cosh(x/4).^13+20818214.*cosh(x/4).^15+14048786.*cosh(x/4).^17-4409026.*cosh(x/4).^19-19030068*cosh(x/4).^21+46003792.*cosh(x/4).^23+10034944.*cosh(x/4).^25- 46183616.*cosh(x/4).^27-11517056.*cosh(x/4).^29+16566784.*cosh(x/4).^31+3445248.*cosh(x/4).^33+ 4956672.*cosh(x/4).^35-1250304.*cosh(x/4).^37+4407296.*cosh(x/4).^39-6324224.*cosh(x/4).^41+ 262144.*cosh(x/4).^43+262144.*cosh(x/4).^45)./(4194304.*cosh(x/4).^47); 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=exact;
Z2=u4;

figure
hZ1 = plot3(t,x,Z1,'-r');
hold on
hZ2 = plot3(t,x,Z2,'-g');
hold off
grid on
xlabel('x') 
ylabel('u')
title('plot3')
legend([hZ1(1),hZ2(1)], 'Z_1','Z_2', 'Location','NE')

figure
hZ1 = plot3(t,x,Z1,'-r');
hold on
hZ2 = plot3(t,x,Z2,'-g');
hold off
grid on
xlabel('x') 
ylabel('u')
title('plot3 (2D Version With Rotation)')
view(90,0)
legend([hZ1(1),hZ2(1)], 'Z_1','Z_2', 'Location','best')

figure
surf(t,x,Z1,'FaceAlpha',0.5)
hold on
surf(t,x,Z2,'FaceAlpha',0.5)
hold off
xlabel('x') 
ylabel('u')
title('surf')

Please edit your code so that it is readable, with each assignment or command on a separate line. It took a few minutes to go through this and parse it that way so that I could understand it.

EDIT — (31 Jul 2021 at 14:18)

Added ‘plot3 (2D Version With Rotation)’ plot.

.

[Omorodion Solomon]

Please does that means that the graph CANNOT be in the form of the attached photo.

[Star Strider]

If you want to plot it as a funciton of ‘x’, the plot calls must be different. Your code uses 3 arguments to plot, and that implies a 3D plot.

Try this —

alpha=1;
t=0.004; 
[x,t] = meshgrid(-4:0.1:4, 0.1:.2:0.4) 

x = 2×81

-4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000 -4.0000 -3.9000 -3.8000 -3.7000 -3.6000 -3.5000 -3.4000 -3.3000 -3.2000 -3.1000 -3.0000 -2.9000 -2.8000 -2.7000 -2.6000 -2.5000 -2.4000 -2.3000 -2.2000 -2.1000 -2.0000 -1.9000 -1.8000 -1.7000 -1.6000 -1.5000 -1.4000 -1.3000 -1.2000 -1.1000

t = 2×81

0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000

exact=(sech(x/4-t/4)).^2; 
f0=(sech(x/4)).^2; 
f1=(sinh(x/4).*(cosh(x/4).^2+1))./(2.*cosh(x/4).^5); 
f2= ((2.*sinh(x/4)+2.*cosh(x/4).^5+sinh(x/4).^3).*(cosh(x/4).^2+2.*cosh(x/4).^4-5))./(16.*cosh(x/4).^11); 
f3= (486.*cosh(x/4).^4.*sinh(x/4)-150.*cosh(x/4).^2.*sinh(x/4)-275.*sinh(x/4)+240.*cosh(x/4).^6.*sinh(x/4)-259.*cosh(x/4).^8.*sinh(x/4)+486.*cosh(x/4).^10.*sinh(x/4)-160.*cosh(x/4).^12.*sinh(x/4)-288.*cosh(x/4).^14.*sinh(x/4)-912.*cosh(x/4).^16.*sinh(x/4)+160.*cosh(x/4).^18.*sinh(x/4)+ 128.*cosh(x/4).^20.*sinh(x/4)-850.*cosh(x/4).^5+ 350.*cosh(x/4).^7+1174.*cosh(x/4).^9+514.*cosh(x/4).^1 -668.*cosh(x/4).^13-776.*cosh(x/4).^15+176.*cosh(x/4).^17+128.*cosh(x/4).^19)./(1024.*cosh(x/4).^23); 
f4=(6873300.*cosh(x/4).^4.*sinh(x/4)-151250.*cosh(x/4).^2.*sinh(x/4)-1739375.*sinh(x/4)+ 660000.*cosh(x/4).^6.*sinh(x/4)-11104474.*cosh(x/4).^8.*sinh(x/4)[phone].*cosh(x/4).^10.*sinh(x/4)-5089324.*cosh(x/4).^12.*sinh(x/4)-42875520.*cosh(x/4).^14.*sinh(x/4)-3455535.*cosh(x/4).^16.*sinh(x/4)+ 56411614.*cosh(x/4).^18.*sinh(x/4)[phone].*cosh(x/4).^20.*sinh(x/4)-31724640.*cosh(x/4).^22.*sinh(x/4)- 36843664.*cosh(x/4).^24.*sinh(x/4)+ 13863840.*cosh(x/4).^26.*sinh(x/4)-13521024.*cosh(x/4).^28.*sinh(x/4)+8647168.*cosh(x/4).^30.*sinh(x/4) [phone].*cosh(x/4).^32.*sinh(x/4)[phone].*cosh(x/4).^34.*sinh(x/4)- 7403520.*cosh(x/4).^36.*sinh(x/4)-7286784.*cosh(x/4).^38.*sinh(x/4)+1155072.*cosh(x/4).^40.*sinh(x/4)+ 557056.*cosh(x/4).^42.*sinh(x/4)-9583750.*cosh(x/4).^5+8131250*cosh(x/4).^7+30360150.*cosh(x/4).^9-16086950.*cosh(x/4).^11-44329262.*cosh(x/4).^13+20818214.*cosh(x/4).^15+14048786.*cosh(x/4).^17-4409026.*cosh(x/4).^19-19030068*cosh(x/4).^21+46003792.*cosh(x/4).^23+10034944.*cosh(x/4).^25- 46183616.*cosh(x/4).^27-11517056.*cosh(x/4).^29+16566784.*cosh(x/4).^31+3445248.*cosh(x/4).^33+ 4956672.*cosh(x/4).^35-1250304.*cosh(x/4).^37+4407296.*cosh(x/4).^39-6324224.*cosh(x/4).^41+ 262144.*cosh(x/4).^43+262144.*cosh(x/4).^45)./(4194304.*cosh(x/4).^47); 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=exact

Z1 = 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

Z2=u4

Z2 = 2×81

0.3976 0.4130 0.4287 0.4448 0.4613 0.4781 0.4952 0.5127 0.5304 0.5483 0.5666 0.5850 0.6036 0.6223 0.6411 0.6600 0.6789 0.6978 0.7166 0.7354 0.7539 0.7722 0.7902 0.8079 0.8252 0.8420 0.8583 0.8740 0.8891 0.9034 0.3547 0.3684 0.3825 0.3970 0.4118 0.4270 0.4425 0.4583 0.4745 0.4910 0.5078 0.5249 0.5423 0.5599 0.5777 0.5958 0.6140 0.6324 0.6509 0.6695 0.6881 0.7068 0.7254 0.7440 0.7624 0.7807 0.7987 0.8164 0.8337 0.8506

figure
hZ1 = plot(x,Z1,'-r');
hold on
hZ2 = plot(x,Z2,'-g');
hold off
grid on
xlabel('x') 
ylabel('u')
title('(2x81) Arrays')
legend([hZ1(1),hZ2(1)], 'Z_1','Z_2', 'Location','best')

figure
hZ1 = plot(x,sum(Z1),'-r');
hold on
hZ2 = plot(x,sum(Z2),'-g');
hold off
grid on
xlabel('x') 
ylabel('u')
title('Summed Over ‘t’')
legend([hZ1(1),hZ2(1)], 'Z_1','Z_2', 'Location','best')

One of these should be what you want.

.

[Omorodion Solomon]

Please can you assist me on this:

</matlabcentral/answers/uploaded_files/717849/IMG_20210821_154014_507.jpg> The numerical results are not corresponding. Here is my code:

alpha=0.25; r=5; t=0.002; x=[-5:0.2:5]; k = reshape(0:100, 1, 1, []); A=exp(x); B =(t.^(k.*alpha))./factorial(k).*alpha.^k; C = sum(B,3); Numerical=A.*C; Exact=A.*exp((r-4).*(t.^alpha)./(alpha)); Z1=Numerical; Z2=Exact; hZ1 = plot(x,Z1,'-r'); hold on hZ2 = plot(x,Z2,'-g'); hold off grid on xlabel('x') ylabel('u') legend([hZ1(1),hZ2(1)], 'CFRDTM','EXACT', 'Location','NE')

[Omorodion Solomon]

[Star Strider]

There are several typographical errors, at lelast with respect to the code representing the symbolic equations in the image.

With those corrections, ‘Numerical’ and ‘Exact’ are the same (within floating-point approximation error), at least for the values provided.

alpha=0.25; 
r=5; 
t=0.002; 
x=[-5:0.2:5]; 
k = reshape(0:100, 1, 1, []); 
A=exp(x); 
% B =(t.^(k.*alpha))./(factorial(k).*alpha.^k); 
B = (t.^(k.*alpha)).*(r-4).^k ./ (factorial(k).*alpha.^k); 
C = sum(B,3); 
Numerical=A.*C; 
% Exact=A.*exp((r-4).*(t.^alpha)./(alpha)); 
Exact = exp(x+((r-4).*(t.^alpha)./(alpha))); 
Z1=Numerical 

Z1 = 1×51

0.0157 0.0192 0.0234 0.0286 0.0349 0.0427 0.0521 0.0637 0.0778 0.0950 0.1160 0.1417 0.1731 0.2114 0.2582 0.3153 0.3852 0.4704 0.5746 0.7018 0.8572 1.0470 1.2788 1.5619 1.9077 2.3301 2.8460 3.4761 4.2457 5.1857

Z2=Exact 

Z2 = 1×51

0.0157 0.0192 0.0234 0.0286 0.0349 0.0427 0.0521 0.0637 0.0778 0.0950 0.1160 0.1417 0.1731 0.2114 0.2582 0.3153 0.3852 0.4704 0.5746 0.7018 0.8572 1.0470 1.2788 1.5619 1.9077 2.3301 2.8460 3.4761 4.2457 5.1857

Error = Numerical - Exact;
ErrorRMS = sqrt(mean(Error.^2))

ErrorRMS = 1.1945e-14

figure
hZ1 = plot(x,Z1,'-r'); 
hold on 
hZ2 = plot(x,Z2,'--g');                                     % Change To Dashed Line
hold off 
grid on 
xlabel('x')  
ylabel('u') 
legend([hZ1(1),hZ2(1)], 'CFRDTM','EXACT', 'Location','NE')          

It would also help if the code was parsed into different lines (as I had to do here), in order for it to run.

.

Answer 2

[Cris LaPierre]

See MATLAB Onramp Ch 9

Answer 3

[Omorodion Solomon]

Yes, you assisted me in solving it last week and I'm grateful. However, I was told to plot a 2D graph of the approximate and exact solution for alpha= 1 and t=0.005. Please I need your assistance again.

[Omorodion Solomon]

This works ! Thanks alot!