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A compact adaptive approach for degenerate singular reaction‐diffusion equations
Author(s) -
Ge Yongbin,
Cai Zhiquan,
Sheng Qin
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22250
Subject(s) - degenerate energy levels , mathematics , reaction–diffusion system , gravitational singularity , partial differential equation , nonlinear system , mathematical analysis , diffusion , physics , quantum mechanics , thermodynamics
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.