微分方程求解

1. 欧拉方法

通过计算：

　　

求[a,b]上的初值问题 y'=f(t,y)，y(a)=y₀的近似解。

function E=euler(f,a,b,ya,M)
%Input  - f is the function entered  as a string 'f'
%       - a and b are the left and right end points
%       - ya is the initial condition y(a)
%       - M is the number of steps
%Output - E=[T' Y'] where T is the vector of abscissas and
%         Y is the vector of ordinates
h=(b-a)/M;
Y=zeros(1,M+1);
T=a:h:b;
Y(1)=ya;
for j=1:M
    Y(j+1)=Y(j+h*feval(f,T(j),Y(j)));
end
E=[T' Y'];
end