Matlab:椭圆方程的导数边值问题

 tic;
 clear
 clc
 N=;
 M=*N;
 h1=/M;
 h2=/N;
 x=:h1:;
 y=:h2:;
 fun=inline('exp(x)*sin(pi*y)','x','y');
 f=inline('(pi^2-1)*exp(x)*sin(pi*y)','x','y');
 lamda1=inline('','y');
 lamda2=inline('2*y','y');
 lamda3=inline('2*x','x');
 lamda4=inline('x^2','x');
 kesai1=inline('','y');
 kesai2=inline('exp(2)*(1+2*y)*sin(pi*y)','y');
 kesai3=inline('-pi*exp(x)','x');
 kesai4=inline('-pi*exp(x)','x');
 numerical=zeros(M+,N+);
 Numerical=numerical;
 error=eye(M+,N+);
 while norm(error,inf) >= 1e-
 for j=:N+
     for i=:M+
         if i== & j==
             Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i+,j)+/h2^*numerical(i,j+)+/h1*kesai1(y(j))+/h2*kesai3(x(i)))...
                 /(/h1^+/h2^+/h1*lamda1(y(j))+/h2*lamda3(x(i)));%U(,)
         elseif i==M+ & j==
              Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h2^*numerical(i,j+)+/h1*kesai2(y(j))+/h2*kesai3(x(i)))...
                 /(/h1^+/h2^+/h1*lamda2(y(j))+/h2*lamda3(x(i)));%U(m,)
         elseif i== & j==N+
             Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i+,j)+/h2^*numerical(i,j-)+/h1*kesai1(y(j))+/h2*kesai4(x(i)))...
                 /(/h1^+/h2^+/h1*lamda1(y(j))+/h2*lamda4(x(i)));%U(,n)
         elseif i==M+ & j==N+
             Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h2^*numerical(i,j-)+/h1*kesai2(y(j))+/h2*kesai4(x(i)))...
                 /(/h1^+/h2^+/h1*lamda2(y(j))+/h2*lamda4(x(i)));%U(m,n)
         elseif i== & j>= & j<=N  %  0j
             Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i+,j)+/h2^*numerical(i,j-)+/h2^*numerical(i,j+)+/h1*kesai1(y(j)))...
                 /(/h1^+/h2^+/h1*lamda1(y(j)));
         elseif j== & i>= & i<=M  % i0
              Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h1^*numerical(i+,j)+/h2^*numerical(i,j+)+/h2*kesai3(x(i)))...
                 /(/h1^+/h2^+/h2*lamda3(x(i)));
         elseif i==M+ & j>= & j<=N  %  mj
              Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h2^*numerical(i,j-)+/h2^*numerical(i,j+)+/h1*kesai2(y(j)))...
                 /(/h1^+/h2^+/h1*lamda2(y(j)));
         elseif j==N+ & i>= & i<=M  %  in
              Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h1^*numerical(i+,j)+/h2^*numerical(i,j-)+/h2*kesai4(x(i)))...
                 /(/h1^+/h2^+/h2*lamda4(x(i)));
         else
              Numerical(i,j)=(f(x(i),y(j))+/h1^*numerical(i-,j)+/h2^*numerical(i,j-)+/h1^*numerical(i+,j)+/h2^*numerical(i,j+))...
                  /(/h1^+/h2^);
         end
     end
 end
 error=Numerical-numerical;
    numerical=Numerical;
 end
 for i=:length(x)
     for j=:length(y)
    Accurate(i,j)=fun(x(i),y(j));
     end
 end
 Error=Accurate'-Numerical';
 [X,Y]=meshgrid(x,y);
 subplot(,,)
 mesh(X,Y,Accurate');
 xlabel('x');ylabel('y');zlabel('Accurate');
 grid on
 subplot(,,)
 mesh(X,Y,Numerical');
 xlabel('x');ylabel('y');zlabel('Numerical');
 grid on
 subplot(,,)
 mesh(X,Y,Error);
 xlabel('x');ylabel('y');zlabel('error');
 grid on
 toc;