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Positivity preserving scheme based on exponential integrators

Author

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  • Korkut, Sıla Ö.
  • Erdoğan, Utku

Abstract

Many phenomena in almost all areas of natural and engineering science are modelled by nonlinear differential equations. However, most of the explicit methods for time integration of nonlinear models fail to preserve some qualitative properties such as positivity of solutions. The major purpose of this study is to suggest a new explicit positivity preserving numerical method based on the exponential integrators. It is shown that the proposed method preserves the positivity of exact solution. Several examples are illustrated to confirm the theoretical result.

Suggested Citation

  • Korkut, Sıla Ö. & Erdoğan, Utku, 2018. "Positivity preserving scheme based on exponential integrators," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 731-739.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:731-739
    DOI: 10.1016/j.amc.2017.10.027
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    References listed on IDEAS

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    1. 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.
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