A fast compact time integrator method for a family of general order semilinear evolution equations

In this paper we develop a fast compact time integrator method for numerically solving a family of general order semilinear evolution equations in regular domains. The spatial discretization is carried out by a fourth-order accurate compact difference scheme in which fast Fourier transform can be utilized for efficient implementation. The resulting semidiscretized problem consists of a system of ordinary differential equations whose solution can be explicitly expressed in term of time integrators, and a desired numerical method is then obtained by further adopting multistep approximations of the nonlinear terms based on the solution formula. Linear stability analysis is performed for the method for secondorder in time evolution equations. Extensive numerical experiments with applications are also presented to demonstrate efficiency, accuracy, and stability of the proposed method in practice. (C) 2019 Elsevier Inc. All rights reserved.