A class of compact boundary value methods applied to semi-linear reaction–diffusion equations

作者：

Highlights：

• This paper deals with a class of compact boundary value methods (CBVMs) for semi-linear reaction-diffusion equations.

• The CBVMs are constructed by combining a 4-ord compact difference method in space with the p-ord boundary value methods in time.

• The results on local stability, unique solvability and convergence of the CBVMs are derived.

• The numerical experiments verify the efficiency and accuracy of the CBVMs.

摘要

•This paper deals with a class of compact boundary value methods (CBVMs) for semi-linear reaction-diffusion equations.•The CBVMs are constructed by combining a 4-ord compact difference method in space with the p-ord boundary value methods in time.•The results on local stability, unique solvability and convergence of the CBVMs are derived.•The numerical experiments verify the efficiency and accuracy of the CBVMs.

论文关键词：Semi-linear reaction-diffusion equations,Compact difference method,Boundary value methods,Unique solvability,Error analysis,Numerical experiment

论文评审过程：Received 30 July 2017, Revised 16 November 2017, Accepted 16 December 2017, Available online 2 January 2018, Version of Record 2 January 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2017.12.033