tydirichlet.m

在matlab环境下用Diriclet与Richardson算法解决偏微分方程的算法实现

function tydirichlet(a,b,c,d,f,g,m,n,e)
u=ones(m+1,n+1);
h1=(b-a)/m;
h2=(d-c)/n;
x=zeros(m+1,1);
y=zeros(n+1,1);
for i=1:m+1
    x(i)=a+h1*(i-1);
end
for i=1:n+1
    y(i)=c+h2*(i-1);
end
[u,u0]=jacobidiedai(f,m,n,h1,h2,u,x,y);
k=0;
while(norm(u-u0,inf)>=e&&k<=1000)
    u=u0;
    [u,u0]=jacobidiedai(f,m,n,h1,h2,u,x,y);
    k=k+1;
end
for i=1:m+1
    for j=1:n+1
        v(i,j)=g(x(i),y(j));
    end
end
    w=abs(u0-v);
subplot(1,2,1);mesh(w)
xlabel('x');
ylabel('y');
zlabel('|u0-v|');
title('误差');
subplot(1,2,2);mesh(u0)