Numerical evaluation of a combination of IMEX and finite difference methods for the solution of the BCRE model

Abstract

In this paper we present a numerical comparison of time integration methods using the finite difference method as spatial discretization to approximate the solution of a pair of coupled partial differential equations that model the dynamics of a sand pile surface. Given the non-linear nature of the model equations, in addition to having diffusion terms, time integration requires a higher computational cost when applying totally explicit or totally implicit schemes, due to this, a study of schemes that combine the methods is carried out. implicit and explicit methods which show a reduction in computational cost while maintaining precision. For each method, the theoretical convergence rate was verified. In the LI-IMEX schemes, a considerable improvement in execution time was obtained.