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Two boundedness and monotonicity preserving methods for a generalized Fisher-KPP equation

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  • Qin, Wendi
  • Ding, Deqiong
  • Ding, Xiaohua

Abstract

A semi-explicit finite difference method and an implicit finite difference method are proposed for a generalized Fisher-KPP equation with two space variables. It is proved that these two methods could preserve the skew-symmetry of this equation. Moreover, under a condition on the step sizes, the semi-explicit method is capable of preserving the positivity, the boundedness, and the spatial and temporal monotonicity of initial approximations. And the implicit method is able to preserve these properties with no restriction on the step sizes. The stability and convergence of these two methods are also analyzed respectively. Finally, some numerical simulations are provided to verify the validity of our analytical results.

Suggested Citation

  • Qin, Wendi & Ding, Deqiong & Ding, Xiaohua, 2015. "Two boundedness and monotonicity preserving methods for a generalized Fisher-KPP equation," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 552-567.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:552-567
    DOI: 10.1016/j.amc.2014.12.043
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    Cited by:

    1. Deng, Dingwen & Xiong, Xiaohong, 2024. "Explicit, non-negativity-preserving and maximum-principle-satisfying finite difference scheme for the nonlinear Fisher's equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Macías-Díaz, J.E. & Hendy, A.S. & De Staelen, R.H., 2018. "A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 1-14.
    3. Yan, Jingye & Zhang, Hong & Liu, Ziyuan & Song, Songhe, 2020. "Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    4. Sapa, Lucjan, 2018. "Difference methods for parabolic equations with Robin condition," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 794-811.
    5. Macías-Díaz, J.E., 2018. "A numerically efficient Hamiltonian method for fractional wave equations," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 231-248.

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