如何在 ODE 中插入列表: [英] How to insert list in a ODE:

问题描述

我正在尝试数值求解以下 ODE

I am trying to numerically solve the following ODE

有边界条件

y(x=0)=0;y(x=20)=1

其中 f(x) 是我已经通过数值求解的另一个 ODE 的解.我正在尝试使用 解决我的 ODEhttps://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.solve_bvp.html，但我遇到的问题是 f(x) 被写成列表

Where f(x) is the solution of another ODE that I already solved numerically. I am trying to solve my ODE with https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.solve_bvp.html, but the problem that I have is that f(x) is written as a list for

 coordinates x = np.arange(0,20.01,0.05)

而且我不知道如何在 scipy.integrate.solve_bvp 中插入列表以获得 ODE 的解.

and I do not know how to insert the list in scipy.integrate.solve_bvp to obtain the solution of ODE.

提前致谢

推荐答案

最好的办法是解决耦合系统，也就是将f的DE与当前DE同时集成.如果这是您之前在 math.SE 上的问题的变体，那么这种耦合方法是不可避免的.

The best way is to solve the coupled system, that is to integrate the DE for f at the same time as the current DE. If this is a variant of your previous problem on math.SE then this coupled approach is unavoidable.

至于字面解，使用插值

def f(x): return numpy.interp(x, x_samples, f_samples)

然后在ODE函数中调用这个函数

and then call this function in the ODE function

def y_ODE(x,y): return [y[1], -0.5*f(x)*y[1]]

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