# How to solve numerically the following non-linear mixed Volterra-Fredholm integral equations system?

I'm looking for an algorithm for solving numerically, for u(t) and v(t), the following system:

$$u(t)=u_{0}-ct+\int_{0}^{t}\frac{a}{1+b_{1}e^{u(s)}+b_{2}e^{v(s)}}ds$$ $$v(t)=v_{0}-Ct+\frac{CT}{\int_{0}^{T}\frac{A}{1+B(e^{u(s)}+e^{v(s)})}ds}\int_{0}^{t}\frac{A}{1+B(e^{u(s)}+e^{v(s)})}ds$$

Ideally with code in Matlab, Maple or Python.

• What have you tried? – Maxim Umansky Apr 10 at 4:26
• Found a piece of Maple code that solves a related problem - a system of second kind Volterra equations (code: maplesoft.com/applications/view.aspx?SID=1622, documentation at: researchgate.net/publication/…). It uses the Newton algorithm to find a numerical solution. I tried to extend it to Volterra-Fredholm systems, but the generalization is not straightforward. Regards, Haplea Ioan Stefan. – Ioan Stefan Haplea Apr 12 at 13:25