I have a system of coupled ODEs that I want to solve. The functions are A(x), B(x), C(x). It is a boundary values problem. I am using Matlab bvp4c.
So far I am not satisfied with my solutions. For the boundaries that are of interest for me, the solver fail (Matlab return "a singular Jacobian encountered"). For some other boundaries, the result depend of the initial guess. So I think that my system is ill defined. I am thinking of adding one constraint but I don't find how to implement it
How to enforce $\int_{a}^{b}d x(A(x)+B(x)+C(x))=N$ ?