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?

1

# Integrating a differential-functional equation

I need to solve a differential-functional equation:

$\partial_t x_m(t,s) = \sum_n A_{mn} x_n(t,s) + \int_0^t \sum_n \sum_{n'} B_{mnn'}(t,s') x_n(t,s) x_{n'}(t,s') ds'$

What is the best numerical procedure?