matlab code for crank nicolson scheme of finite difference method

Dear sir,

I am trying to solve the finite difference methof for crank nicolson scheme to 2d heat equation. please let me know if you have any MATLAB CODE for this

boundary condition are

If you can kindly send me the matlab code, it will be very useful for my research work . thank you very much.

below is the code i tried. kindly correct the code for given the FDs

clear all; clc;

L = 1.;

T =1.;

maxk = 1500; % Number of time steps

dt = T/maxk;

n = 16; % Number of space steps

dx =0.5

dy =0.5

nn=3

mm=3

X=1

M=0.5

N=0.4

for i = 1:n;

for j = 1:n;

x(i) =(i-1)*dx;

Uk(i,j,1) =0;

Vk(i,j,1) =5;

Ck(i,j,1) =5;

Tk(i,j,1) =50;

end

end

% % Temperature at the boundary (T=0)

for k=1:maxk;

for j=1:n-1;

Uk(1,j,k) = 0;%sin(i*j);

Vk(1,j,k)= 0;

Tk(1,j,k)= 0;

Ck(1,j,k)= 0;

Uk(n+1,j,k) = 0;

Vk(n+1,j,k) = 0;

Tk(i,j+1,k+1)=Tk(i,j-1,k+1)+Tk(i,j+1,k)-Tk(i,j-1,k)+(x(j).^nn)*4*dy;

Ck(i,j+1,k+1)=Ck(i,j-1,k+1)+Ck(i,j+1,k)-Ck(i,j-1,k)+(x(j).^mm)*4*dy;

% Tk(n+1,j,k) = i*j

% Ck(n+1,j,k) = 50.;

time(k) = (k-1)*dt;

end

end

% Implementation of the explicit method

for k=1:maxk-1 % Time Loop

for i=2:n-1; % Space Loop

for j=2:n-1;

Uk(i,j,k)= Uk(i,j-1,k+1).*[-Vk(i,j,k).*dt/4.*dy-dt/2.*dy.*dy]...

+Uk(i,j,k+1).*(1+Uk(i,j,k).*dt/2.*dx+dt/dy.*dy+M.*dt/2)...

+Uk(i,j+1,k+1).*[Vk(i,j,k).*dt/4.*dy-dt/2.*dy^2]...

+Uk(i,j,k).*[((Uk(i-1,j,k+1)-Uk(i,j,k)+Uk(i-1,j,k)).*dt)/2.*dx]...

-Vk(i,j,k).*[((Uk(i,j-1,k)-Uk(i,j+1,k)).*dt)/4.*dy]...

-[((Tk(i,j,k+1)+Tk(i,j,k))/2+ N.*(Ck(i,j,k+1)+Ck(i,j,k))/2).*dt].*cos(pi)...

+[(( Uk(i,j-1,k)-2.* Uk(i,j,k)+ Uk(i,j+1,k))/2.*dy.*dy).*dt]...

+M.* Uk(i,j,k);

end

end

%Uk(i+1,j+1,k+1)=Uk(i,j,k)+dx*m

end

% Graphical representation of the temperature at different selected times

figure(1)

plot(x,Uk(:,:,1),'-r',x,Uk(:,:,3),'-b',x,Uk(:,:,5),'-y',x,Uk(:,:,10),'-g')

[NOUFA]

Dear Sir,

if you know about how to solve the finite difference methof for crank nicolson scheme to1d heat equation. please let me know if you have any CODE for this.

many thanks

Answer 1

[priya m priya m]

Sir, have you got error in above code corrected? if corrected kindly share the corrected code , it would be helpful for me.

[priya m priya m]

Sir, have you got error in above code corrected? if corrected kindly share the corrected code , it would be helpful for me.