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A class of second-order and dynamically consistent nonstandard finite difference schemes for nonlinear Volterra’s population growth model

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Abstract

In a recent work (Hoang in Math Comput Simul 199:359–373, 2022), a class of nonstandard finite difference (NSFD) schemes preserving the positivity and boundedness of the nonlinear Volterra integro-differential population growth model has been constructed. However, these NSFD schemes are only convergent of order one. In this work, we introduce a new class of second-order and dynamically consistent NSFD schemes derived from non-local approximations in combination with modified denominator functions. It is proved that the constructed NSFD schemes are not only convergent of order two but also dynamically consistent with respect to the positivity and boundedness of the Volterra’s population growth model. As an important application, we combine the second-order NSFD schemes with Richardson’s extrapolation method to generate higher-accuracy numerical solutions. Consequently, higher-accuracy numerical solutions for the population growth model can be obtained easily. Finally, a set of numerical examples is reported to support the theoretical findings.

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Acknowledgements

We would like to thank the editor and anonymous referees for useful and valuable comments that led to a great improvement of the paper.

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  1. Department of Mathematics, FPT University, Hoa Lac Hi-Tech Park, Km29 Thang Long Blvd, Hanoi, Viet Nam

    Manh Tuan Hoang

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  1. Manh Tuan Hoang
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Correspondence to Manh Tuan Hoang.

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Communicated by Zhaosheng Feng.

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Hoang, M.T. A class of second-order and dynamically consistent nonstandard finite difference schemes for nonlinear Volterra’s population growth model. Comp. Appl. Math. 42, 85 (2023). https://doi.org/10.1007/s40314-023-02230-z

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