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
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Omorodion Solomon
el 31 de Jul. de 2021
Comentada: Star Strider
el 21 de Ag. de 2021
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)+17738388.*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)+31975008.*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) +13020672.*cosh(x/4).^32.*sinh(x/4)+11695104.*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')
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Star Strider
el 31 de Jul. de 2021
Editada: Star Strider
el 31 de Jul. de 2021
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)+17738388.*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)+31975008.*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) +13020672.*cosh(x/4).^32.*sinh(x/4)+11695104.*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.
.
5 comentarios
Star Strider
el 21 de Ag. de 2021
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
Z2=Exact
Error = Numerical - Exact;
ErrorRMS = sqrt(mean(Error.^2))
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.
.
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