Preservative Splitting Numerical Schemes for Solving a Variable Coefficient Quenching Problem

Physical processes are modelled mathematically using Partial Differential Equations(PDEs). An insight into these processes requires solving those PDEs. Since these equations most of the time do not have analytical solutions, delicate numerical methods are required. In this talk, we will explore the numerical solution of the two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The differential equation possesses a variable diffusion coefficient and a nonlinear forcing term that leads to a strong quenching singularity. Our current investigation focuses on the construction of a finite difference implementation of a Peaceman- Rachford and a Glowinski-Le Tallec splitting procedures for solving the aforementioned problem. Temporal adaptation is implemented through arc-length estimations of the rate-of- change of the numerical solution. The positivity, monotonicity and localized linear stability of the splitting schemes are analyzed.