the code print -inf in TT matrix. Please anyone helps

clear all

close all

clc

%Geometry definition

L=0.3; %Length of the The rectangular bar in meter

W=0.4; %Width of the The rectangular bar in meter

%Material properties

alpha=11.234E-05; %theraml diffusivity

% computional details

i_max=31; %max divisions in x-direction

j_max=41; %max divisions in y-direction

req_error=0.01; %total variation condition in temp

delta_t=1; %time step

delta_x=L/(i_max-1); %Divisons in x-direction

delta_y=W/(j_max-1); %Divisons in y-direction

d=alpha*delta_t/(delta_x)^2;%Defining stability condition

%Solution initializing

T=zeros(i_max,j_max);

% Boundary conditions

T(:,1)=40;

T(:,j_max)=10;

TT=T;

%processing

error_mag=1;

iterations=0;

while error_mag > req_error

for i=2:(i_max-1)

for j=(2:j_max-1)

TT(i,j)=T(i,j)+d*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1)-4*T(i,j));

end

end

iterations=iterations+1;

error_mag = 0;

for i=2:(i_max-1)

for j=2:(j_max-1)

error_mag =error_mag +abs(T(i,j)-TT(i,j)); %defining the total variance to calcualte the difference in temperature from one time level to the next

error_track(iterations)= error_mag;

end

end

if rem(iterations,1000)==0

iterations

error_mag

end

T=TT;

end

%plottting the solution

solution_x=linspace(0,0.3,7);

solution_y=linspace(0,0.4,41);

T_final = T(1:5:i_max,:);

[X,Y] = meshgrid(solution_x,solution_y);

T_1_ss=T(11,:);

%figure(1);

%contourf(X,Y,T_final.')

%colorbar

%colormap(jet)

title('Steady state Solution of FTCS Explicit scheme ')

xlabel('L')

ylabel('W')

figure(2);

plot(solution_y,T_1_ss)

title('Steady stateSolution of FTCS Explicit scheme')

xlabel('Y')

ylabel('Temperature')

Answer 1

[Torsten]

Your value of 1 for delta_t violates the CFL condition for stability of the explicit Euler scheme.

Choose a value that satisfies CFL.