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Difference methods for parabolic equations with Robin condition

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  • Sapa, Lucjan

Abstract

Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with the Robin condition are approximated in the paper by solutions of associated boundedness-preserving implicit difference functional equations. It is proved that the discrete solutions uniquely exist, they are uniformly bounded with respect to meshes and the numerical method is convergent and stable. We also find the error estimate and its asymptotic behavior. The properties of some auxiliary nonlinear discrete recurrent equations are showed. The proofs are based on the comparison technique and the Banach fixed-point theorem.

Suggested Citation

  • Sapa, Lucjan, 2018. "Difference methods for parabolic equations with Robin condition," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 794-811.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:794-811
    DOI: 10.1016/j.amc.2017.10.061
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hazrat Ali & Md. Kamrujjaman & Md. Shafiqul Islam, 2022. "An Advanced Galerkin Approach to Solve the Nonlinear \\[6pt]Reaction-Diffusion Equations With Different Boundary Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(1), pages 1-30, March.

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