Spectral semi-discretization algorithm for a class of nonlinear parabolic PDEs with applications

作者：

Highlights：

• Developing a practical and efficient hybrid spectral collocation method for a class of time-dependent parabolic PDEs.

• Utilizing the alternative generalized Laguerre basis functions (with positive coefficients) and a giving a proof of the convergence.

• Showing the superiority of the developed technique for the biological model problems (FitzHugh–Nagumo and Newell–Whitehead equations) especially using a larger time step.

摘要

•Developing a practical and efficient hybrid spectral collocation method for a class of time-dependent parabolic PDEs.•Utilizing the alternative generalized Laguerre basis functions (with positive coefficients) and a giving a proof of the convergence.•Showing the superiority of the developed technique for the biological model problems (FitzHugh–Nagumo and Newell–Whitehead equations) especially using a larger time step.

论文关键词：Alternative Laguerre functions,Collocation method,Parabolic PDEs,Taylor series expansion

论文评审过程：Received 15 October 2021, Revised 1 March 2022, Accepted 4 May 2022, Available online 14 May 2022, Version of Record 14 May 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127226