I need to solve a differential-functional equation:


$\partial\_t x\_m(t,s) = \sum\_n A\_{mn} x\_n(t,s) + \int\_0^t \sum\_n \sum\_{n'} B\_{mnn'}(t,s') x\_n(t,s) x\_{n'}(t,s') ds'$


with $t > s$ and initial condition $x\_m(t,t) = C\_m$.


What is the best numerical procedure?



Integrating a differential-functional equation
I have solved it in a trivial way: using Euler discretization in the $t$ direction and trapezoid quadrature in $s$ direction, with equal steps. Works quite well for the data I use.


