A fast compact exponential time differencing method for semilinear parabolic equations with Neumann boundary conditions. (August 2019)

• Record Type: Journal Article
• Authors: Huang, Jianguo; Ju, Lili; Wu, Bo
• Is Part Of: Applied mathematics letters. Volume 94(2019)
• Page Start: 257
• Page End: 265
• Publication Date: 2019-08
• Subjects: Semilinear parabolic equations -- Compact difference scheme -- Neumann boundary condition -- Exponential integrator -- Fast Fourier transform; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.03.012
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper we propose a fast compact exponential time differencing method for solving a class of semilinear parabolic equations with Neumann boundary conditions. The model equation is first discretized in space by a fourth-order compact finite difference scheme with an appropriate treatment of the boundary condition, the resulting semi-discretized system is then diagonalized with fast Fourier transforms, and further expressed in a temporal integral formulation by the use of exponential integrators according to the Duhamel principle. The fully discrete scheme is finally obtained by using multistep interpolations for the nonlinear terms and exact evaluations of the underlying integrals. Some numerical experiments are performed to demonstrate the accuracy and efficiency of the proposed method.