Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour

Bürger, Raimund; Inzunza, Daniel; Mulet, Pep; Villada, Luis M.

Abstract

The numerical solution of nonlinear convection-diffusion equations with nonlocal flux by explicit finite difference methods is costly due to the local spatial convolution within the convective numerical flux and the disadvantageous Courant-Friedrichs-Lewy (CFL) condition caused by the diffusion term. More efficient numerical methods are obtained by applying second-order implicit-explicit (IMEX) Runge-Kutta time discretizations to an available explicit scheme for such models in Carrillo et al. (2015) [13]. The resulting IMEX-RK methods require solving nonlinear algebraic systems in every time step. It is proven, for a general number of space dimensions, that this method is well defined. Numerical experiments for spatially two-dimensional problems motivated by models of collective behaviour are conducted with several alternative choices of the pair of RungeKutta schemes defining an IMEX-RK method. For fine discretizations, 1MEX-RK methods turn out more efficient in terms of reduction of error versus CPU time than the original explicit method. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

Más información

Título según WOS: Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour
Título según SCOPUS: Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour
Título de la Revista: APPLIED NUMERICAL MATHEMATICS
Volumen: 144
Editorial: Elsevier
Fecha de publicación: 2019
Página de inicio: 234
Página final: 252
Idioma: English
DOI:

10.1016/j.apnum.2019.04.018

Notas: ISI, SCOPUS