Topics in matrix analysis
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
Scientific Computing and Differential Equations: An Introduction to Numerical Methods
A Moving Mesh Method Based on the Geometric Conservation Law
SIAM Journal on Scientific Computing
Blow-up in a reactive-diffusive medium with a moving heat source
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
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
Preface: Splitting methods for differential equations
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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Various types of partial differential equations have been playing increasingly important roles in the study of theoretical and numerical combustion. In this paper, we are particularly concerned with the numerical solution of certain premixed model problems in rectangular spatial domains. The two-dimensional reaction-diffusion equations involved are associated with an ignition type nonlinearity involving a mathematical degeneracy at a corner point. A Peaceman-Rachford-Strang splitting based adaptive method is proposed on exponentially evolving grids. Rigorous numerical analysis are given to ensure the satisfactory effectiveness, efficiency, and numerical stability of the algorithm developed. Simulation experiments are provided to illustrate our accomplishments.