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 Runge-Kutta schemes defining an IMEX-RK method. For fine discretizations, IMEX-RK methods turn out more efficient in terms of reduction of error versus CPU time than the original explicit method.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.