A compact adaptive approach for degenerate singular reaction‐diffusion equations. Issue 4 (19th February 2018)

• Record Type: Journal Article
• Authors: Ge, Yongbin; Cai, Zhiquan; Sheng, Qin
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 4(2018)
• Page Start: 1166
• Page End: 1187
• Publication Date: 2018-02-19
• Subjects: adaptations -- compact methods -- degeneracy -- order of approximations -- quenching blow‐up -- singular reaction‐diffusion equations -- stability; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22250
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : This article concerns a compact adaptive method for the numerical solution of nonlinear degenerate singular reaction‐diffusion equations. The partial differential equation problems exhibit strong quenching blow‐up type singularities, and are critical in numerous applications ranging from optimized internal combustion designs to oil pipeline decay predictions. Adaptive schemes of fourth order in space and second order in time are acquired and discussed. Nonuniform spatial and temporal grids are utilized through suitable adaptations. Rigorous analysis is given for the numerical stability, and computational experiments are performed to illustrate our conclusions.