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Universal approaches to approximate biological systems with nonstandard finite difference methods

Author

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  • Wood, Daniel T.
  • Kojouharov, Hristo V.
  • Dimitrov, Dobromir T.

Abstract

Nonstandard finite difference methods have been extensively used to numerically solve various problems in science and engineering. Most of those methods have been specifically designed to handle each problem separately and have been difficult to extend to other problems. In recent years, general nonstandard modeling approaches preserving key characteristics of autonomous dynamical systems have been proposed. In this paper, three of these numerical methods are presented and their performance is evaluated and compared in several different settings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:133:y:2017:i:c:p:337-350
    DOI: 10.1016/j.matcom.2016.04.007
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    References listed on IDEAS

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    1. Dimitrov, Dobromir T. & Kojouharov, Hristo V., 2005. "Analysis and numerical simulation of phytoplankton–nutrient systems with nutrient loss," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 33-43.
    2. Dimitrov, Dobromir T. & Kojouharov, Hristo V., 2008. "Nonstandard finite-difference methods for predator–prey models with general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 1-11.
    3. 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.
    4. Mickens, Ronald E., 2007. "Determination of denominator functions for a NSFD scheme for the Fisher PDE with linear advection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 190-195.
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    Cited by:

    1. Carlos Julio Mayorga & María Ángeles Castro & Antonio Sirvent & Francisco Rodríguez, 2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models," Mathematics, MDPI, vol. 11(8), pages 1-9, April.
    2. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    4. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

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