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A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion

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  • Mickens, Ronald E.

Abstract

We construct a discrete model for a particular PDE having nonlinear advection, diffusion, and reaction. The use of the author’s nonstandard finite difference methods form the basis for this construction. We demonstrate that the solutions to the scheme satisfy positivity and boundedness conditions. Further, an explicit functional relation between the time and space step-sizes is obtained. A discussion is given as to how these results can be generalized to a broad class of PDE’s having these same structural properties.

Suggested Citation

  • Mickens, Ronald E., 2005. "A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 439-446.
    • Handle: RePEc:eee:matcom:v:69:y:2005:i:5:p:439-446
    DOI: 10.1016/j.matcom.2005.03.008
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    Cited by:

    1. Mandel, Jan & Bennethum, Lynn S. & Beezley, Jonathan D. & Coen, Janice L. & Douglas, Craig C. & Kim, Minjeong & Vodacek, Anthony, 2008. "A wildland fire model with data assimilation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 584-606.
    2. Wood, Daniel T. & Kojouharov, Hristo V. & Dimitrov, Dobromir T., 2017. "Universal approaches to approximate biological systems with nonstandard finite difference methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 337-350.
    3. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.

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