Implicit-Explicit Multistep Finite Element Methods for Some Nonlinear Reaction-Diffusion Equations

Abstract

隐–显多步有限元方法是近年来提出的一种方法，主要用于非线性抛物问题。我们对一类非线性反应扩散方程的初边值问题进行近似，给出了隐–显多步有限元方法的逼近格式，并证明了该格式的最优阶误差估计。 Implicit-explicit multistep methods were recently proposed, and mainly used to nonlinearparabolicequa- tions. We approximate the solution of initial boundary value problems for some nonlinear reaction-diffusion Equations, and discretize by Implicit-Explicit Multistep finite element methods. The optimal order error esti- mates is derived in this paper.