四阶阿当姆斯显式解初值问题matlab
时间: 2024-01-12 16:22:17 浏览: 39
以下是使用四阶Adams预报校正方法和四阶Runge-Kutta方法求解常微分方程的MATLAB代码示例:
1. 使用四阶Adams预报校正方法求解常微分方程的MATLAB代码示例(文件名:CAdams4PC.m):
```matlab
function A = CAdams4PC(f, a, b, N, ya)
h = (b - a) / N;
t = a:h:b;
A = zeros(1, N+1);
A(1) = ya;
for i = 1:3
k1 = h * feval(f, t(i), A(i));
k2 = h * feval(f, t(i) + h/2, A(i) + k1/2);
k3 = h * feval(f, t(i) + h/2, A(i) + k2/2);
k4 = h * feval(f, t(i) + h, A(i) + k3);
A(i+1) = A(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;
end
for i = 4:N
A(i+1) = A(i) + h * (55 * feval(f, t(i), A(i)) - 59 * feval(f, t(i-1), A(i-1)) + 37 * feval(f, t(i-2), A(i-2)) - 9 * feval(f, t(i-3), A(i-3))) / 24;
A(i+1) = A(i) + h * (9 * feval(f, t(i+1), A(i+1)) + 19 * feval(f, t(i), A(i)) - 5 * feval(f, t(i-1), A(i-1)) + feval(f, t(i-2), A(i-2))) / 24;
end
end
```
2. 使用四阶Runge-Kutta方法求解常微分方程的MATLAB代码示例(文件名:RungKutta4.m):
```matlab
function R = RungKutta4(f, a, b, N, ya)
h = (b - a) / N;
t = a:h:b;
R = zeros(1, N+1);
R(1) = ya;
for i = 1:N
k1 = h * feval(f, t(i), R(i));
k2 = h * feval(f, t(i) + h/2, R(i) + k1/2);
k3 = h * feval(f, t(i) + h/2, R(i) + k2/2);
k4 = h * feval(f, t(i) + h, R(i) + k3);
R(i+1) = R(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;
end
end
```