Moving mesh methods based on moving mesh partial differential equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Moving Mesh Methods for Problems with Blow-up
SIAM Journal on Scientific Computing
r-refinement for evolutionary PDEs with finite elements or finite differences
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
Blowup in diffusion equations: a survey
Journal of Computational and Applied Mathematics - Special issue: nonlinear problems with blow-up solutions: applications and numerical analysis
The influence of two moving heat sources on blow-up in a reactive-diffusive medium
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Scaling invariance and adaptivity
Applied Numerical Mathematics
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
Precise computations of chemotactic collapse using moving mesh methods
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
A moving mesh method with variable mesh relaxation time
Applied Numerical Mathematics
Efficient computation of dendritic growth with r-adaptive finite element methods
Journal of Computational Physics
Journal of Computational Physics
Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method
Journal of Computational and Applied Mathematics
Moving mesh methods for blowup in reaction-diffusion equations with traveling heat source
Journal of Computational Physics
Moving mesh method for problems with blow-up on unbounded domains
Numerical Algorithms
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This paper studies the numerical solution of a reaction-diffusion differential equation with traveling heat sources. According to the fact that the locations of heat sources are known, we add auxiliary mesh points exactly at heat sources and present a novel moving mesh algorithm for solving the problem. Several examples are provided to demonstrate the efficiency of the new moving mesh method, especially in the case of two or three traveling heat sources. Moreover, numerical results illustrate that the speed of the movement of the heat source is critical for blow-up when there is only one traveling heat source. For the case of two traveling heat sources, blow-up depends not only on the speed but also on the distance between the two traveling heat sources.