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1、%%%%真解u=sin(pi*x)*sin(pi*y)%%%%%%%方程-Laplace(u)=f%%%%%%%%%%f=2*pi^2*sin(pi*x)*sin(pi*y)%%%%%%%%%%differencecodeforellipticequationswithconstantcoefficient%%%%%clear%clcN=20;h=1/N;S=h^2;x=0:h:1;y=0:h:1;%%%StiffmatrixA=zeros((N-1)^2,(N-1)^2);fori=1A(i,i)=4/h^2;A(i,i
2、+1)=-1/h^2;A(i,i+(N-1))=-1/h^2;endfori=N-1A(i,i-1)=-1/h^2;A(i,i)=4/h^2;A(i,2*i)=-1/h^2;%A(i,i+(N-1))=-1/h^2endfori=(N-2)*(N-1)+1A(i,i-(N-1))=-1/h^2;A(i,i)=4/h^2;A(i,i+1)=-1/h^2;endfori=(N-1)^2A(i,i-(N-1))=-1/h^2;A(i,i)=4/h^2;A(i,i-1)=-1/h^2;endforn=2:N-2i=(N-2)*(N
3、-1)+n;A(i,i-(N-1))=-1/h^2;A(i,i-1)=-1/h^2;A(i,i)=4/h^2;A(i,i+1)=-1/h^2;endfori=2:N-2A(i,i-1)=-1/h^2;A(i,i)=4/h^2;A(i,i+1)=-1/h^2;A(i,i+(N-1))=-1/h^2;endform=1:N-3i=m*(N-1)+1;A(i,i-(N-1))=-1/h^2;A(i,i)=4/h^2;A(i,i+1)=-1/h^2;A(i,i+(N-1))=-1/h^2;endform=2:N-2i=m*(N-1
4、);A(i,i-(N-1))=-1/h^2;A(i,i-1)=-1/h^2;A(i,i)=4/h^2;A(i,i+(N-1))=-1/h^2;end%form=1:N-3%i=m*(N-1)+(N-1);%A(i,i-(N-1))=-1/h^2;%A(i,i-1)=-1/h^2;%A(i,i)=4/h^2;%A(i,i+(N-1))=-1/h^2;%endform=1:N-3forn=2:N-2i=m*(N-1)+n;A(i,i-(N-1))=-1/h^2;A(i,i-1)=-1/h^2;A(i,i)=4/h^2;A(i,
5、i+1)=-1/h^2;A(i,i+(N-1))=-1/h^2;endend%%%RighttermF=zeros((N-1)^2,1);form=0:N-2forn=1:N-1i=m*(N-1)+n;F(i)=2*pi^2*sin(pi*n*h)*sin(pi*(m+1)*h);endEndU=zeros((N-1)^2,1);U=AF;U1=zeros((N+1)^2,1);form=1:N-1U1(m*(N+1)+2:m*(N+1)+N)=U((m-1)*(N-1)+1:m*(N-1));endplot(x,y,U
6、1,’-k’)U-exact=inline(‘sin(xx(:,1).*sin(xx(:,2))’,’xx’);%真解plot(x,y,U-exact,’-r’)Err=max(abs(U1-U-exact));%最大模L2-err=norm(U1-U-exact)*h;%L2errorErrL2-err%%%%真解u=sin(pi*x)*sin(pi*y)%%%%%%%方程-Laplace(u)=f%%%%%%%%%%f=2*pi^2*sin(pi*x)*sin(pi*y)%%%%%%%%%%compactdiffere
7、ncecodeforellipticequationswithconstantcoefficient%%%%%clear%clcN=20;h=1/N;S=h^2;x=0:h:1;y=0:h:1;%%%StiffmatrixA=zeros((N-1)^2,(N-1)^2);B=zeros((N-1)^2,(N-1)^2);F=zeros((N-1)^2,1);fori=1A(i,i)=10/(3*h^2);A(i,i+1)=-2/(3*h^2);A(i,i+(N-1))=-2/(3*h^2);A(i,i+(N-1)+1)=-
8、1/(6*h^2);B(i,i)=25/36;B(i,i+1)=5/72;B(i,i+(N-1))=5/72;B(i,i+(N-1)+1)=1/144;endfori=N-1A(i,i-1)=-2/(3*h^2);A(i,i)=10/(3*h^2);A(i,i+(N-1)-1)=-1/(6*h^2);A
