An adaptive Rothe method for nonlinear reaction-diffusion systems
Selected papers of the sixth conference on Numerical Treatment of Differential Equations
Moving Mesh Methods for Problems with Blow-up
SIAM Journal on Scientific Computing
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume I
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman-Rachford Splitting
SIAM Journal on Scientific Computing
A splitting moving mesh method for reaction-diffusion equations of quenching type
Journal of Computational Physics
Numerical quenching for the semilinear heat equation with a singular absorption
Journal of Computational and Applied Mathematics
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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.