matlab求解Charney方程
时间: 2023-09-02 22:07:01 浏览: 29
Charney方程是一个二维非线性偏微分方程,可以使用MATLAB中的偏微分方程求解器PDE Toolbox来求解。具体步骤如下:
1. 定义Charney方程的偏微分方程:
```
function [c,f,s] = charneypde(x,t,u,DuDx)
c = 1;
f = DuDx(1);
s = -DuDx(2) - u*DuDx(1);
end
```
2. 定义Charney方程的初始条件和边界条件:
```
function [pl,ql,pr,qr] = charneybc(xl,ul,xr,ur,t)
pl = [ul(1)];
ql = [0];
pr = [0; ur(2)];
qr = [1; 0];
end
```
3. 定义求解域:
```
x = linspace(0,1,100);
t = linspace(0,1,100);
```
4. 调用PDE Toolbox的求解函数pdepe进行求解:
```
sol = pdepe(0,@charneypde,@charneybc,@charneyic,x,t);
```
其中@charneypde是Charney方程的偏微分方程函数,@charneybc是Charney方程的边界条件函数,@charneyic是Charney方程的初始条件函数。
5. 可视化结果:
```
u = sol(:,:,1);
surf(x,t,u)
xlabel('x')
ylabel('t')
zlabel('u')
```
完整的MATLAB代码如下:
```
function charney
x = linspace(0,1,100);
t = linspace(0,1,100);
sol = pdepe(0,@charneypde,@charneybc,@charneyic,x,t);
u = sol(:,:,1);
surf(x,t,u)
xlabel('x')
ylabel('t')
zlabel('u')
end
function [c,f,s] = charneypde(x,t,u,DuDx)
c = 1;
f = DuDx(1);
s = -DuDx(2) - u*DuDx(1);
end
function [pl,ql,pr,qr] = charneybc(xl,ul,xr,ur,t)
pl = [ul(1)];
ql = [0];
pr = [0; ur(2)];
qr = [1; 0];
end
function u0 = charneyic(x)
u0 = [sin(pi*x); 0];
end
```