谁知道matlab怎么求解偏微分方程的解析解啊
{:soso_e101:}
求救啊 {:soso_e113:} 建议用其他软件。。
这是网上找的。。符号求解，还是别用MATLAB..
china19901015 发表于 2011-8-16 21:13 static/image/common/back.gif
建议用其他软件。。
这是网上找的。。符号求解，还是别用MATLAB..
符号求解用什么软件呢:o {:3_41:}{:3_41:}maple azure5566 发表于 2011-8-17 11:05 static/image/common/back.gif
maple
maple可以求解析解吗{:3_48:} hanmeng8 发表于 2011-8-17 14:21 static/image/common/back.gif
maple可以求解析解吗
可以，实际上matlab的符号运算用的就是maple的内核 顶一下。。。。。。。。。{:3_50:} 这个很像传热学中的傅里叶方程。感觉不是很好解……我在书上只找到了泊松方程的运算程序，还是二维的，贴上来看看，不知道对你有没有帮助。
function = poisson(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter)
%solve u_xx + u_yy + g(x,y)u = f(x,y)
% over the region D = = {(x,y) |x0 <= x <= xf, y0 <= y <= yf}
% with the boundary Conditions:
% u(x0,y) = bx0(y), u(xf,y) = bxf(y)
% u(x,y0) = by0(x), u(x,yf) = byf(x)
% Mx = # of subintervals along x axis
% My = # of subintervals along y axis
% tol : error tolerance
% MaxIter: the maximum # of iterations
x0 = D(1); xf = D(2); y0 = D(3); yf = D(4);
dx = (xf - x0)/Mx; x = x0 + *dx;
dy = (yf - y0)/My; y = y0 + ’*dy;
Mx1 = Mx + 1; My1 = My + 1;
%Boundary conditions
for m = 1:My1, u(m,)=; end %left/right side
for n = 1:Mx1, u(,n) = ; end %bottom/top
%initialize as the average of boundary values
sum_of_bv = sum(sum() u(,2:Mx)’]));
u(2:My,2:Mx) = sum_of_bv/(2*(Mx + My - 2));
for i = 1:My
for j = 1:Mx
F(i,j) = f(x(j),y(i)); G(i,j) = g(x(j),y(i));
end
end
dx2 = dx*dx; dy2 = dy*dy; dxy2 = 2*(dx2 + dy2);
rx = dx2/dxy2; ry = dy2/dxy2; rxy = rx*dy2;
for itr = 1:MaxIter
for j = 2:Mx
for i = 2:My
u(i,j) = ry*(u(i,j + 1)+u(i,j - 1)) + rx*(u(i + 1,j)+u(i - 1,j))...
+ rxy*(G(i,j)*u(i,j)- F(i,j)); %Eq.(9.1.5a)
end
end
if itr > 1 & max(max(abs(u - u0))) < tol, break; end
u0 = u;
end
以上是possion.m文件，下面给个例子。
%solve_poisson in Example 9.1
f = inline(’0’,’x’,’y’); g = inline(’0’,’x’,’y’);
x0 = 0; xf = 4; Mx = 20; y0 = 0; yf = 4; My = 20;
bx0 = inline(’exp(y) - cos(y)’,’y’); %(E9.1.2a)
bxf = inline(’exp(y)*cos(4) - exp(4)*cos(y)’,’y’); %(E9.1.2b)
by0 = inline(’cos(x) - exp(x)’,’x’); %(E9.1.3a)
byf = inline(’exp(4)*cos(x) - exp(x)*cos(4)’,’x’); %(E9.1.3b)
D = ; MaxIter = 500; tol = 1e-4;
= poisson(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter);
clf, mesh(x,y,U), axis() 困死了。。