Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 20, Issue 5, Pages 639-649Publisher
WILEY-BLACKWELL
DOI: 10.1002/num.20003
Keywords
Maxwell-Cattaneo law; nonstandard finite difference scheme; damped wave equation; positivity
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A positivity-preserving nonstandard finite difference scheme is constructed to solve an initial-boundary value problem involving heat transfer described by the Maxwell-Cattaneo thermal conduction law, i.e., a modified form of the classical Fourier flux relation. The resulting heat transport equation is the damped wave equation, a PDE of hyperbolic type. In addition, exact analytical solutions are given, special cases are mentioned, and it is noted that the positivity condition is equivalent to the usual linear stability criteria. Finally, solution profiles are plotted and possible extensions to a delayed diffusion equation and nonlinear reaction-diffusion systems are discussed. (C) 2004 Wiley Periodicals, Inc.
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