How to solve system of nonlinear ODEs with "unusual" boundary conditions?

Hello, everyone!

I have got a problem with solving a 2nd order system of nonlinear ODEs. I want to solve numerically the system below :

The problem is in "unusual" boundary conditions, determined below :

Conditions are dermined at the beginning and end of the interval (not a classical Cauchy problem). I have no idea how to solve a system with such conditions via MatLab. Could anyone help me, please ? Or give a link to example how to solve similar problem?

Best, Andrii.

[Alan Stevens]

cot(0) is infinite, which makes your first equation difficult to get started!

[Andrii Syrota]

Yes, the boundary condition was wrong , thank you (i have corrected it) . But i am interested in method in general, how to solve a system with such conditions.

Answer 1

[J. Alex Lee]

If you are talking about boundary value problems versus initial value problems, look at bvp4c and bvp5c. There is nothing "unusual" about that.

For your equations specifically, if you can't express as a system explicit equations in first derivatives, then neither of those functions may work; I don't know if there are built-in solvers in Matlab for that, but recall seeing similar questions in this forum.

https://www.mathworks.com/matlabcentral/answers/478652-solving-bvp-for-dae-in-matlab

A straightforward way to solve could be to discretize the equations using finite differences on some domain and solve as a set of nonlinear algebraic equations.

[Andrii Syrota]

Thank you very much!