使用matlab解偏微分方程

使用MATLAB解偏微分方程可以通过函数pdepe来实现。pdepe函数是MATLAB自带的偏微分方程的工具箱函数之一。下面是解偏微分方程的一种实现代码：

function first
%计算从t:0~3的值
x = linspace(0,1,20);
t = linspace(0,3,60);

subplot(121);
sol = pdepe(0,@firstPdefun,@firstIcfun,@firstBcfun,x,t);
u = surf(x,t,sol(:,:,1));
title('微分方程数值解');
xlabel('x');
ylabel('t');
zlabel('u')

subplot(122);
[X,T = meshgrid(x,t);
U = exp(-T).*sin(pi*X);
surf(X,T,U);
title('微分方程解析解');
end

%方程段
function [c,f,s = firstPdefun(x,t,u,dudx)
c = pi^2;
f = dudx;
s = 0;
end

%起始值条件段
function u = firstIcfun(x)
u = sin(pi*x);
end

%边界条件段
function [pl,ql,pr,qr = firstBcfun(xl,ul,xr,ur,t)
pl = ul;
ql = 0;
pr = pi*exp(-t);
qr = 1;
end

这段代码会计算在时间范围t：0~3，空间范围x：0~1内的偏微分方程的数值解，并将结果以3D图形的形式显示出来。同时也计算了解析解，并在另一个子图中以3D图形的形式显示出来。<span class="em">1</span><span class="em">2</span><span class="em">3</span>
#### 引用[.reference_title]
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