A parameter robust numerical method for a nonlinear system of singularly perturbed elliptic equations

摘要

This paper deals with a parameter robust numerical method for solving a nonlinear singularly perturbed reaction-diffusion system of elliptic equations. Existence and uniqueness of a solution to the nonlinear system of elliptic equations are presented. Existence and uniqueness of a solution to a nonlinear difference scheme, which approximates the nonlinear elliptic system, are established. The uniform convergence of the nonlinear difference scheme on piecewise uniform and log-meshes to the solution of the nonlinear elliptic system is established. A monotone iterative method for solving the nonlinear difference scheme is given. The uniform convergence of monotone iterates to the solutions of the nonlinear difference scheme and to the nonlinear elliptic system is proved. Numerical experiments confirm the established theoretical results. (C) 2020 Elsevier B.V. All rights reserved.