MATLAB: Help in solving an error

errorhelppoisson

hi guys,
i found this program on matlab and tried to modifie the boundary condition but it tells me that there is an error and i tried to figure how to solve it but i didn't know how
so if someone could help me i will be very thankfull.

Best Answer

Hi,
try:
% Solving the 2-D Poisson equation by the Finite Difference
...Method 
% Numerical scheme used is a second order central difference in space
...(5-point difference)
%%





%Specifying parameters
nx=80;                           %Number of steps in space(x)
ny=80;                           %Number of steps in space(y)       
niter=1000;                      %Number of iterations 
dx=2/(nx-1);                     %Width of space step(x)
dy=2/(ny-1);                     %Width of space step(y)
x=0:dx:2;                        %Range of x(0,2) and specifying the grid points
y=0:dy:2;                        %Range of y(0,2) and specifying the grid points
b=zeros(nx,ny);                  %Preallocating b
pn=zeros(nx,ny);                 %Preallocating pn
%%
% Initial Conditions
p=zeros(nx,ny);                  %Preallocating p
%%
%Boundary conditions
p(:,1)=0;
p(:,ny)=0;
p(1,:)=0;                  
p(nx,:)=0;
%%
%Source term
for i=2:nx-1
    for j=2:ny-1
        b(i,j)=sin((pi/3)*i).*sin((pi/3)*j);
    end
end
%%
i=2:nx-1;
j=2:ny-1;
%Explicit iterative scheme with C.D in space (5-point difference)
for it=1:niter
    pn=p;
    p(i,j)=((dy^2*(pn(i+1,j)+pn(i-1,j)))+(dx^2*(pn(i,j+1)+pn(i,j-1)))-(b(i,j)*dx^2*dy*2))/(2*(dx^2+dy^2));
    %Boundary conditions 
    p(:,1)=0;
    p(:,ny)=0;
    p(1,:)=0;                  
    p(nx,:)=0;
end
%%
%Plotting the solution
h=surf(x,y,p','EdgeColor','none');       
shading interp
axis([-0.5 2.5 -0.5 2.5 -100 100])
title({'2-D Poisson equation';['{\itNumber of iterations} = ',num2str(it)]})
xlabel('Spatial co-ordinate (x) \rightarrow')
ylabel('{\leftarrow} Spatial co-ordinate (y)')
zlabel('Solution profile (P) \rightarrow')
Best regards
Stephan
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