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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.

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    $\begingroup$ What have you tried? $\endgroup$ – Maxim Umansky Apr 10 at 4:26
  • $\begingroup$ 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. $\endgroup$ – Ioan Stefan Haplea Apr 12 at 13:25

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