二步四阶线性多步法求解常微分问题u ′ (x) = −5u, u(0) = 1, 0 < x < 1,步长为0.1,并且输出x对应的u值的matlab程序程序
时间: 2023-11-28 16:49:03 浏览: 93
以下是使用二步四阶线性多步法求解常微分问题的matlab程序:
```matlab
function u = twoStepFourOrderMethod()
% 定义初始条件
u0 = 1;
x0 = 0;
xEnd = 1;
h = 0.1;
% 计算步数
n = (xEnd - x0) / h;
% 初始化u和x
u = zeros(1, n+1);
x = zeros(1, n+1);
u(1) = u0;
x(1) = x0;
% 使用欧拉法计算第一个点
u(2) = u(1) + h * (-5 * u(1));
x(2) = x(1) + h;
% 使用二步四阶线性多步法计算剩余点
for i = 3:n+1
u(i) = u(i-2) + 4*h/3*(-5*u(i-1)) - h/3*(-5*u(i-2));
x(i) = x(i-1) + h;
end
% 输出结果
for i = 1:n+1
fprintf('x = %.1f, u = %.4f\n', x(i), u(i));
end
end
```
运行该程序,将会输出每个点对应的x和u值。
阅读全文
相关推荐


















