richardson.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 [E]=richardson(t,h,f,z,a,b,c,s)
m=1/h;n=1/t;
r=(c*t)/(h*h);
for i=1:m+1
    x(i)=(i-1)*h;
    u(i,1)=z(x(i));
end
for i=1:n+1
    y(i)=(i-1)*t;
    u(1,i)=a(y(i));
    u(m+1,i)=b(y(i));
end
for i=2:m
    u(i,2)=z(x(i))+t*(c*(z(x(i-1))-2*z(x(i))+z(x(i+1)))/(h*h)+f(x(i),0));
end
A(1,1)=-4*r;A(1,2)=2*r;A(m-1,m-2)=2*r;A(m-1,m-1)=-4*r;
for i=2:m-2
    A(i,i)=-4*r;A(i,i-1)=2*r;A(i,i+1)=2*r;
end
for k=2:n
    for i=1:m-1
        d(i)=u(i+1,k);
    end
    for i=2:m-2
        e(i)=t*f(x(i+1),y(k))+u(i+1,k-1);
    end
    e(1)=2*t*f(x(2),y(k))+2*r*u(1,k)+u(2,k-1);
    e(m-1)=2*t*f(x(m),y(k))+2*r*u(m+1,k)+u(m,k-1);
    v=A*d'+e';
for i=2:m
    u(i,k+1)=v(i-1);
end
end
x1=u(51,11:10:101)
x2=s(0.5,0.1:0.1:1)
E=abs(x1-x2)