MATLAB解一阶微分方程

MATLAB里ode45命令用4阶龙格-库塔解一阶微分方程（常系数/变系数）都能解。

首先把微分方程化为dx/dt = f(x)的标准形式写成函数放在一个文件里，再写主程序用ode45调用这个文件。举例如下：

函数文件：方程的定义（一定要用函数名命名）

% di/dt = L-1u - L-1(WL+R)i
function iprime = hw11_2(t,i)
L = [.0072, 0, 0, .1, .0054, 0;
    0, .007, 0, 0, 0, .0026;
    0, 0, .001, 0, 0, 0;
    1.5*.1, 0, 0, 2.5, .125, 0;
    1.5*.0054, 0, 0, .125, .0068, 0;
    0, 1.5*.0026, 0, 0, 0, .0016];
W = zeros(6,6);
W(1,2) = -100*pi;
W(2,1) = 100*pi;
R = diag([.002,.002,.002,.4,.015,.015]);
u = zeros(6,1);
u(4) = 400;
iprime = L\u - L\(W*L+R)*i;

主程序文件：调用ode45

% solve function hw11_2
theta0 = 0;
h = 1e-3;                       % step
i0 = zeros(1,6);
i0(4) = 400/.4;
ts = 0:h:1;                     % time span
[t,i] = ode45('hw11_2',ts,i0);  % solve
thetaA = 100*pi*ts + theta0;
thetaB = thetaA - pi/3*2;
thetaC = thetaA + pi/3*2;
n = length(ts);
ia = zeros(n,1);
ib = zeros(n,1);
ic = zeros(n,1);
% inverse Park transform
for j = 1:n
    tt = ts(j);
    thetaA = 100*pi*tt + theta0;
    thetaB = thetaA - 2*pi/3;
    thetaC = thetaA + 2*pi/3;
    ia(j) = cos(thetaA)*i(j,1) - sin(thetaA)*i(j,2) + i(j,3);
    ib(j) = cos(thetaB)*i(j,1) - sin(thetaB)*i(j,2) + i(j,3);
    ic(j) = cos(thetaC)*i(j,1) - sin(thetaC)*i(j,2) + i(j,3);
end
figure(1);
plot(ts,ia,'y',ts,ib,'g',ts,ic,'r');
title(['three phase short circuit (\theta_0 = ',num2str(theta0),')']);
xlabel('t/s');ylabel('i/A');
legend('I_a','I_b','I_c');
absia = abs(ia);
[iamax,jamax] = max(absia);
tamax = ts(jamax);