Please use this identifier to cite or link to this item: https://doi.org/10.1137/S1064827501380691
Title: Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting
Authors: Cheng, H.
Lin, P. 
Sheng, Q.
Tan, R.C.E. 
Keywords: Degeneracy
Linear stabilities
Monotonicity
Nonlinear reaction-diffusion equations
Quenching singularity
Semidis-cretization
Splitting
Time adaptation
Issue Date: 2003
Citation: Cheng, H., Lin, P., Sheng, Q., Tan, R.C.E. (2003). Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting. SIAM Journal on Scientific Computing 25 (4) : 1273-1292. ScholarBank@NUS Repository. https://doi.org/10.1137/S1064827501380691
Abstract: This paper studies the numerical solution of two-dimensional nonlinear degenerate reaction-diffusion differential equations with singular forcing terms over rectangular domains. The equations considered may generate strong quenching singularities. This investigation focuses on a variable time step Peaceman-Rachford splitting method for the aforementioned problem. The time adaptation is implemented based on arc-length estimations of the first time derivative of the solution. The two-dimensional problem is split into several one-dimensional problems so that the computational cost is significantly reduced. The monotonicity and localized linear stability of the variable step scheme are investigated. We give some numerical examples to illustrate our results as well as to demonstrate the viability and efficiency of the method over existing methods for the quenching problem. It is also shown that the numerical solution obtained preserves important properties of the physical solution of the given problem.
Source Title: SIAM Journal on Scientific Computing
URI: http://scholarbank.nus.edu.sg/handle/10635/104145
ISSN: 10648275
DOI: 10.1137/S1064827501380691
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