matlab差分模型求解,MATLAB五点差分法解拉普拉斯方程问题

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function u = peEllip5(nx,minx,maxx,ny,miny,maxy)

format long;

hx = (maxx-minx)/(nx-1);

hy = (maxy-miny)/(ny-1);

u0 = zeros(nx,ny);

for j=1:ny

u0(j,1) = EllIni2Uxl(minx,miny+(j-1)*hy);

u0(j,nx) = EllIni2Uxr(maxx,miny+(j-1)*hy);

end

for j=1:nx

u0(1,j) = EllIni2Uyl(minx+(j-1)*hx,miny);

u0(ny,j) = EllIni2Uyr(minx+(j-1)*hx,maxy);

end

A = -4*eye((nx-2)*(ny-2),(nx-2)*(ny-2));

b = zeros((nx-2)*(ny-2),1);

for i=1:(nx-2)*(ny-2)

if mod(i,nx-2) == 1

if i==1

A(1,2) = 1;

A(1,nx-1) = 1;

b(1) = – u0(1,2) – u0(2,1);

else

if i == (ny-3)*(nx-2)+1

A(i,i+1) = 1;

A(i,i-nx+2) = 1;

b(i) = – u0(ny-1,1) – u0(ny,2);

else</