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Moving collocation method for a reaction‐diffusion equation with a traveling heat source
Author(s) -
Liang Kewei,
Zhu Hancan
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21788
Subject(s) - mathematics , partial differential equation , heat equation , domain (mathematical analysis) , collocation method , bounded function , collocation (remote sensing) , dirac delta function , mathematical analysis , diffusion equation , boundary value problem , boundary (topology) , singularity , finite difference method , differential equation , ordinary differential equation , computer science , economy , service (business) , machine learning , economics
We consider a reaction‐diffusion equation with a traveling heat source on an unbounded domain. The numerical simulation of the problem is difficult because of the moving singularity, the blow‐up phenomenon, and the delta function in the equation. Because we are only interested in the solution behavior near the heat source, we choose a bounded moving domain which contains the heat source and has the same speed as the source. Local absorbing boundary conditions are constructed on the boundaries of the moving domain. Then, we transform the moving domain to a fixed one. At last, a special moving collocation method is adopted. The new method is much simpler than the existing moving finite difference methods. Moreover, numerical experiments illustrate the accuracy and efficiency of our moving collocation method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013