Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.apnum.2006.07.018
Title: Numerical solution of quenching problems using mesh-dependent variable temporal steps
Authors: Liang, K.W.
Lin, P. 
Tan, R.C.E. 
Keywords: Adaptive method
Implicit finite difference scheme
Irregular grids
Nonlinear reaction-diffusion equations
Quenching problems
Singularity
Issue Date: May-2007
Citation: Liang, K.W., Lin, P., Tan, R.C.E. (2007-05). Numerical solution of quenching problems using mesh-dependent variable temporal steps. Applied Numerical Mathematics 57 (5-7 SPEC. ISS.) : 791-800. ScholarBank@NUS Repository. https://doi.org/10.1016/j.apnum.2006.07.018
Abstract: In this paper, we introduce a new adaptive method for computing the numerical solutions of a class of quenching parabolic equations which exhibit a solution with one singularity. Our method systematically generates an irregular mesh with mesh-dependent temporal increments based on the solution behavior from which an implicit finite difference scheme associated with the irregular mesh is constructed. The convergence and stability of the finite difference scheme is analyzed for the solution before quenching. An equivalent linearized model is used to justify the stability of the method near quenching as well. A numerical example is provided to demonstrate the viability of the proposed method. © 2006 IMACS.
Source Title: Applied Numerical Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103655
ISSN: 01689274
DOI: 10.1016/j.apnum.2006.07.018
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