matlab偏微分方程的完整代码
时间: 2023-10-31 12:11:59 浏览: 54
这里提供一个求解二维泊松方程的matlab代码示例:
```matlab
% 定义网格
nx = 50;
ny = 50;
dx = 1/nx;
dy = 1/ny;
x = linspace(0,1,nx+2);
y = linspace(0,1,ny+2);
[X,Y] = meshgrid(x,y);
% 定义边界条件
u = zeros(nx+2,ny+2);
u(:,1) = sin(pi*x);
u(:,end) = sin(pi*x)*exp(-pi);
u(1,:) = 0;
u(end,:) = 0;
% 定义右端项
f = -pi^2*sin(pi*X).*sin(pi*Y);
% 迭代求解
tol = 1e-6;
err = 1;
while err > tol
u_old = u;
for i = 2:nx+1
for j = 2:ny+1
u(i,j) = (u(i+1,j) + u(i-1,j) + u(i,j+1) + u(i,j-1) - dx^2*f(i,j))/4;
end
end
err = max(max(abs(u-u_old)));
end
% 可视化结果
figure;
surf(X,Y,u);
xlabel('x');
ylabel('y');
zlabel('u');
title('Solution to Poisson Equation');
```
这个代码使用了简单的迭代法求解二维泊松方程,并且使用了网格有限差分方法离散化。