A particle method for non-local advection-selection-mutation equations
Numerical Analysis
2023-04-28 v1 Numerical Analysis
Abstract
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularised sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite interval is shown and an explicit rate of convergence is given. Furthermore, we investigate the asymptotic-preserving properties of the method in large times, providing sufficient conditions for it to hold true as well as examples and counter-examples. Finally, we illustrate the method in two cases taken from the literature.
Cite
@article{arxiv.2304.14210,
title = {A particle method for non-local advection-selection-mutation equations},
author = {Frank Ernesto Alvarez and Jules Guilberteau},
journal= {arXiv preprint arXiv:2304.14210},
year = {2023}
}