A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems

作者：

Highlights：

• A hybrid asymptotic and augmented high order compact finite volume method is designed for nonlinear singular two point boundary value problems.

• The convergence of the proposed scheme in the whole interval is analyzed and proved.

• By reconstructing the Puiseux series of the solution, it is shown that the high order of convergence of the solution near the singularity is obtained with respect to 2 L norms, 1H semi-norm and L norm.

• An parameter that is related to the singularity of the solution is regarded as an augmented variable. By using this augmented variable, we construct a numerical scheme and simultaneously obtain the values of the augmented variable and the solution.

摘要

•A hybrid asymptotic and augmented high order compact finite volume method is designed for nonlinear singular two point boundary value problems.•The convergence of the proposed scheme in the whole interval is analyzed and proved.•By reconstructing the Puiseux series of the solution, it is shown that the high order of convergence of the solution near the singularity is obtained with respect to 2 L norms, 1H semi-norm and L norm.•An parameter that is related to the singularity of the solution is regarded as an augmented variable. By using this augmented variable, we construct a numerical scheme and simultaneously obtain the values of the augmented variable and the solution.

论文关键词：Nonlinear singular two point boundary value problem,Puiseux series,Compact finite volume method,Augmented variable

论文评审过程：Received 25 September 2018, Revised 6 February 2020, Accepted 10 October 2020, Available online 5 November 2020, Version of Record 5 November 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125745