Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
Mathematics and Computers in Simulation
A splitting moving mesh method for reaction-diffusion equations of quenching type
Journal of Computational Physics
Numerical solution of quenching problems using mesh-dependent variable temporal steps
Applied Numerical Mathematics
An effective z-stretching method for paraxial light beam propagation simulations
Journal of Computational Physics
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Effective stretching strategies for paraxial lightwave propagation simulations
Computers and Structures
A numerical investigation of blow-up in reaction-diffusion problems with traveling heat sources
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Solving degenerate quenching-combustion equations by an adaptive splitting method on evolving grids
Computers and Structures
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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.