清空筛选条件
清空筛选条件

matlab code for crank nicolson scheme of finite difference method

22 次查看（过去 30 天）
Ragul Kumar
Ragul Kumar 2020-11-10
评论： priya m priya m 2022-10-5
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')
  1 个评论
NOUFA
NOUFA 2021-10-2
编辑：NOUFA 2021-10-2
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

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

priya m priya m
priya m priya m 2022-10-5
Sir, have you got error in above code corrected? if corrected kindly share the corrected code , it would be helpful for me.
  1 个评论
priya m priya m
priya m priya m 2022-10-5
Sir, have you got error in above code corrected? if corrected kindly share the corrected code , it would be helpful for me.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Programming 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by