My instructor said you only need to change few things from bottom code to solve

Question

My instructor said you only need to change few things from bottom code to solve this problem

%------------------------------------------------
% Solve the ODE BV problem f_xx + f_yy = 0
% with boundary conditions: f = 1, f = 2,
% f = 3, and f = 4
% using iterative finite difference approach.
%
% Note: we are using i and j here...not cool in
% general.
%------------------------------------------------

clear all
close all
clc

nFrames = 200; % number of frames

[x,y] = meshgrid(0 : 0.04 : 1); % make x-y grid

f = 4*ones(length(x), length(y)); % initialize f values

f(:,1) = 1;
f(:,length(x)) =3; % ...and the boundaries
f(1,:) =2;
f(length(y),:) =4;
for i = 1 : nFrames % for each plot...
  
for j = 2 : (length(y)-1)
for k = 2 : (length(x)-1)
f(k,j) = (f(k-1,j)+f(k+1,j)+f(k,j-1)+f(k,j+1))/4;
end
end
  
  
mesh(x,y,f),... % make one plot
xlabel('X axis'),...
   ylabel('Y axis'),...
   zlabel('F axis'),...
title('The plot title'),...
   axis([0 1 0 1 0 4]);
% axis off
shading interp
  
drawnow

end

beep % hey, I'm done

Please give me the code that works

Explanation / Answer

For checking convergence the solution is stored in two arrays. One is the array f which stores the current iteration solution and another is the fprev which stores solution in previous iteration

Now we calculate maximum value in: abs(fprev-f) and choose that to be the error,e

This makes sense because if the max (abs(fprev-f)) falls below some tolerance then all values of f will will within that : fprev +- tolerance.

And code runs till e falls below some specified tolerance. In code below we have specified:

tolerance = 1e-8

The modified code with convergence criterion is:

%------------------------------------------------
% Solve the ODE BV problem f_xx + f_yy = 0
% with boundary conditions: f = 1, f = 2,
% f = 3, and f = 4
% using iterative finite difference approach.
%
% Note: we are using i and j here...not cool in
% general.
%------------------------------------------------

clear all
close all
clc

nFrames = 200; % number of frames

[x,y] = meshgrid(0 : 0.04 : 1); % make x-y grid

f = 4*ones(length(x), length(y)); % initialize f values

f(:,1) = 1;
f(:,length(x)) =3; % ...and the boundaries
f(1,:) =2;
f(length(y),:) =4;
fprev    = f;
err      = 1;
tolerance=1e-8;
h      = 0.1;
while err > tolerance

for j = 2 : (length(y)-1)
for k = 2 : (length(x)-1)
f(k,j) = (f(k-1,j)+f(k+1,j)+f(k,j-1)+f(k,j+1)-(h^2)*(x(k,j)+y(k,j)))/4;
err    = max(max(abs(fprev-f)));
fprev = f;
end
end

mesh(x,y,f),... % make one plot
xlabel('X axis'),...
   ylabel('Y axis'),...
   zlabel('F axis'),...
title('The plot title'),...
   axis([0 1 0 1 0 4]);
% axis off
shading interp

drawnow

end

beep % hey, I'm done

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