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%波动方程有限差分法 
f=inline('sin(pi*x)','x'); 
g=inline('0'); 
l=1;T=0.5;m=10;N=10;af=1; 
xx=[];tt=[];uu=[]; 
h=l/m; 
k=T/N; 
lmd=k*af/h; 
u(1,2:N+1)=0; 
u(m+1,2:N+1)=0; 
u(1,1)=f(0); 
u(m+1,1)=f(l); 
for i=2:m 
    u(i,1)=f((i-1)*h); 
    u(i,2)=(1-lmd^2)*f((i-1)*h)+lmd^2*(f(i*h)+f((i-2)*h))/2+k*g((i-1)*h); 
end 
for j=2:N 
    for i=2:m 
        u(i,j+1)=2*(1-lmd^2)*u(i,j)+lmd^2*(u(i+1,j)+u(i-1,j))-u(i,j-1); 
    end 
end 
t=linspace(0,T,N+1); 
x=linspace(0,l,m+1); 
for i=1:m+1 
    for j=1:N+1 
        xx=[xx,x(i)]; 
        tt=[tt,t(j)]; 
        uu=[uu,u(i,j)]; 
        tur(i,j)=sin(pi*x(i))*cos(pi*t(j)); 
        ture=[ture,tur(i,j)]; 
    end 
end 
re=[xx'     tt'     uu'      ture']