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)
Matlab.rar_matlab小程序
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Matlab.rar （60个子文件） 
Matlab 
hotqch.m 490B LR.m 750B erfen.m 441B sc.m 468B Taylor解常微分方程.m 415B poisson.m 3KB hermite.m 583B yangtiao.m 425B Newton插值.m 340B Untitled.m 2KB sp.m 212B 追赶法求解三对角方程.m 350B dNeville.m 94B stguass.m 884B fx.m 430B 改进平方根法.m 759B gexian.m 202B zjf.m 1KB 平方根法.m 727B nihe.m 333B tranBB.m 357B sanci.m 813B fc.m 52B lbg.m 429B trisys.m 210B wavequ.m 701B fun.m 52B seidel.m 187B jacobi.m 175B diedai.m 204B newton.m 153B CN.m 681B cgls.m 663B nihe1.m 347B trapr1.m 139B poiss.m 3KB df.m 34B qgauss.m 919B jtf.m 365B euler.m 361B fh.m 27B Euler1.m 653B Langrange.m 423B fg.m 35B giassl.m 786B dEuler.m 78B Untitled9.m 322B ft.m 30B sanci2.m 865B gauss.m 1KB Euler解常微分方程.m 652B hothch.m 349B RK.m 434B xycf.m 1KB fitpt.m 2KB fun1.m 52B fitfun.m 1KB ytiao.m 397B dNewton.m 56B Neville插值.m 241B
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