A compact adaptive approach for degenerate singular reaction‐diffusion equations. Issue 4 (19th February 2018) - Ge, Yongbin; Cai, Zhiquan; Sheng, Qin
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.