Numerical solution of two and three dimensional time fractional damped nonlinear Klein–Gordon equation using ADI spectral element method

作者：

Highlights：

• An efficient numerical method has been developed for solving the two and three dimensional time fractional damped nonlinear Klein–Gordon equation.

• The proposed algorithm is based on the ADI spectral element method.

• The unconditional stability and convergence of the proposed method have been proved.

• Numerical experiments demonstrate the good accuracy and efficiency of the proposed ADI spectral element method.

摘要

•An efficient numerical method has been developed for solving the two and three dimensional time fractional damped nonlinear Klein–Gordon equation.•The proposed algorithm is based on the ADI spectral element method.•The unconditional stability and convergence of the proposed method have been proved.•Numerical experiments demonstrate the good accuracy and efficiency of the proposed ADI spectral element method.

论文关键词：Time fractional,Damped Klein–Gordon equation,Alternating direction implicit method,Unconditionally stability,Error estimate,Legendre spectral element method

论文评审过程：Received 27 June 2020, Revised 23 December 2020, Accepted 4 March 2021, Available online 15 April 2021, Version of Record 15 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126182