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
