matlab迭代求解泊松方程,MATLAB编程求解二维泊松方程

%%%% 真解 u=sin(pi*x)*sin(pi*y) %%%

%%%% 方程 -Laplace(u)=f %%%%%%

%%%% f=2*pi^2*sin(pi*x)*sin(pi*y) %%%%%%

%%%%difference code for elliptic equations with constant coefficient %%%%% %clear all

%clc

N=20;

h=1/N;

S=h^2;

x=0:h:1;

y=0:h:1;

%%% Stiff matrix

A=zeros((N-1)^2,(N-1)^2);

for i=1

A(i,i)=4/h^2;

A(i,i+1)=-1/h^2;

A(i,i+(N-1))=-1/h^2;

end

for i=N-1

A(i,i-1)=-1/h^2;

A(i,i)=4/h^2;

A(i,2*i)=-1/h^2; %A(i,i+(N-1))=-1/h^2

end

for i=(N-2)*(N-1)+1

A(i,i-(N-1))=-1/h^2;

A(i,i)=4/h^2;

A(i,i+1)=-1/h^2;

end

for i=(N-1)^2

A(i,i-(N-1))=-1/h^2;

A(i,i)=4/h^2;

A(i,i-1)=-1/h^2;

end

for n=2:N-2

i=(N-2)*(N-1)+n;

A(i,i-(N-1))=-1/h^2;

A(i,i-1)=-1/h^2;

A(i,i)=4/h^2;

A(i,i+1)=-1/h^2;

end

for i=2:N-2