High-order compact difference scheme of 1D nonlinear degenerate convection–reaction–diffusion equation with adaptive algorithm

Abstract

This research describes a high accuracy adaptive difference strategy on 1D reaction–diffusion equation with convection item, which explains quenching phenomena of nonlinear singular degenerate problem. It originates from the first and the second central difference scheme and the forward difference operator. The former is used to discrete the first-order and the second-order spatial derivative and the latter is utilized to approximate temporal derivative. After its accuracy and stability discussed, the typical quenching cases are illustrated singularity of the nonlinear problem by using the proposed strategy with adaptation mechanism and comparing with the low-order approach.

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Acknowledgments

The authors will thank Prof. Sheng and Prof. Ge for their guidance, and the editor-in-chief and reviewer for their valuable comments.