An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Abstract

This paper deals with nonlinear diffusion problems which include the Stefan problem,  the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages, namely, it is very easy-to-implement, the ensuing linear algebraic systems are symmetric, it requires low computational cost, the accuracy is comparable to that of the well-studied nonlinear schemes, the computation is much faster than the nonlinear schemes to obtain the same level of accuracy. In this paper, numerical experiments are carried out to demonstrate efficiency of the proposed scheme.