Solve a set of ODEs with given initial conditions and final conditions

Question

Akshat Koolwal 2021-3-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/777477-solve-a-set-of-odes-with-given-initial-conditions-and-final-conditions

回答： Bjorn Gustavsson 2021-3-19

I am trying to solve a set of ODEs in MATLAB. I have four different ODEs for four variables and solving them should be easy if we had initial conditions for all the variables. But that's where things get tricky, I have initial conditions for three variables but final condition for the fourth variable. All the traditional solvers are designed to handle IVPs only. What can be the most optimised approach to handle it since I might have to solve the equation multiple times.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Jan 2021-3-19

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/777477-solve-a-set-of-odes-with-given-initial-conditions-and-final-conditions#answer_652392

编辑：Jan 2021-3-19

If you have some initial and some final values, this is not an IVP (initial value problem), but a BVP (boundary value problem). A single oder mutliple shooting appraoch is working then.

There is no "most optimized" approach and you can write a PhD about a solver for a specific problem.

See https://www.mathworks.com/help/matlab/boundary-value-problems.html

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Answer 2

Bjorn Gustavsson 2021-3-19

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/777477-solve-a-set-of-odes-with-given-initial-conditions-and-final-conditions#answer_652397

To me this seems to be a problem that the shooting-method would be suited for. That will require you to solve the problem multiple times, so hopefully it is not too stiff ODEs or too long period of integration. Just set up something like a Newton-Raphson method for testing improved initial guesses for your fourth variable.

HTH