matlab.zip_VU99_thereforeky9

close all; clear all; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%具体实例%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% a=-1;b=1;c=-1;d=1; n=6;m=5;TOL=1e-10; ITMAX=500; %f=inline('x*exp(y)','x','y'); %ga=inline('0','x','y');gb=inline('2*exp(y)','x','y'); %gc=inline('x','x','y');gd=inline('exp(1)*x','x','y'); f=inline('2*pi^2*sin(pi*x)*sin(pi*y)','x','y'); ga=inline('0','x','y');gb=inline('0','x','y'); gc=inline('0','x','y');gd=inline('0','x','y'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%程序部分%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% h=(b-a)/n; k=(d-c)/m; x=linspace(a,b,n+1); x=x(2:n); y=linspace(c,d,m+1); y=y(2:m); u=zeros(n-1,m-1); lmd=h^2/k^2; mu=2*(1+lmd); xx=[]; yy=[]; uu=[]; ture=[]; l=1; while (l<=ITMAX) z=(-h*h*f(x(1),y(m-1))+ga(a,y(m-1))+lmd*gd(x(1),d)+... lmd*u(1,m-2)+u(2,m-1))/mu; NORM=abs(z-u(1,m-1)); u(1,m-1)=z; for i=2:n-2 z=(-h*h*f(x(i),y(m-1))+lmd*gd(x(i),d)+u(i-1,m-1)+... u(i+1,m-1)+lmd*u(i,m-2))/mu; if(abs(u(i,m-1)-z)>NORM) NORM=abs(u(i,m-1)-z); end u(i,m-1)=z; end z=(-h*h*f(x(n-1),y(m-1))+gb(b,y(m-1))+... lmd*gd(x(n-1),d)+u(n-2,m-1)+lmd*u(n-1,m-2))/mu; if(abs(u(n-1,m-1)-z)>NORM) NORM=abs(u(n-1,m-1)-z); end u(n-1,m-1)=z; for j=m-2:-1:2 z=(-h*h*f(x(1),y(i))+ga(a,y(j))+lmd*u(1,j+1)+... lmd*u(1,j-1)+u(2,j))/mu; if(abs(u(1,j)-z)>NORM) NORM=abs(u(1,j)-z); end u(1,j)=z; for i=2:n-2 z=(-h*h*f(x(i),y(j))+u(i-1,j)+lmd*u(i,j+1)+... u(i+1,j)+lmd*u(i,j-1))/mu; if( abs(u(i,j)-z)>NORM) NORM=abs(u(i,j)-z); end u(i,j)=z; end z=(-h*h*f(x(n-1),y(j))+gb(b,y(j))+u(n-2,j)+... lmd*u(n-1,j+1)+lmd*u(n-1,j-1))/mu; if(abs(u(n-1,j)-z)>NORM) NORM=abs(u(n-1,j)-z); end u(n-1,j)=z; end z=(-h*h*f(x(1),y(1))+ga(a,y(1))+lmd*gc(x(1),c)+... lmd*u(1,2)+u(2,1))/mu; if(abs(u(1,1)-z)>NORM) NORM=abs(u(1,1)-z); end u(1,1)=z; for i=2:n-2 z=(-h*h*f(x(i),y(1))+lmd*gc(x(i),c)+... u(i-1,1)+lmd*u(i,2)+u(i+1,1))/mu; if(abs(u(i,1)-z)>NORM) NORM=abs(u(i,1)-z); end u(i,1)=z; end z=(-h*h*f(x(n-1),y(1))+gb(b,y(1))+lmd*gc(x(n-1),c)+... u(n-2,1)+lmd*u(n-1,2))/mu; if(abs(u(n-1,1)-z)>NORM) NORM=abs(u(n-1,1)-z); end u(n-1,1)=z; if(NORM<=TOL) for i=1:n-1 for j=1:m-1 xx=[xx,x(i)]; yy=[yy,y(j)]; uu=[uu,u(i,j)]; %tur(i,j)=x(i)*exp(y(j)); tur(i,j)=-sin(pi*x(i))*sin(pi*y(j)); ture=[ture,tur(i,j)]; end end break; end l=l+1; end re=[xx' yy' uu' ture'] %%%%%%%%%%%%%%%%%%%%%%%问题%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Y,X]=meshgrid(y,x); mesh(X,Y,u)