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Simulation of Riccati Differential Equations by Nonlocal Approximation of Nonlinear Terms and Reconstruction of Denominator Functions

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  • J. Sunday

    (Department of Mathematics, Adamawa State University, Mubi, Nigeria)

  • Y. Skwame

    (Department of Mathematics, Adamawa State University, Mubi, Nigeria)

  • T. Y. Kyagya

    (Department of Mathematics and Statistics, Federal University, Wukari, Nigeria)

Abstract

Two ways to efficiently construct a Non-Standard Finite Difference Method (NSFDM) is to approximate the nonlinear term(s) of the differential equation nonlocally and also to reconstruct the denominator function(s). In this research, we shall simulate a special class of nonlinear differential equations called the Riccati Differential Equations (RDEs) by nonlocally approximating the nonlinear terms and also reconstructing the denominator functions. The need for this approach came up due to some shortcomings of existing methods in which the qualitative properties of the exact solutions are not usually transferred to the numerical (approximate) solutions. The approach developed in this research has the property that its solution does not exhibit numerical instabilities in view of the results generated.

Suggested Citation

  • J. Sunday & Y. Skwame & T. Y. Kyagya, 2017. "Simulation of Riccati Differential Equations by Nonlocal Approximation of Nonlinear Terms and Reconstruction of Denominator Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 3(7), pages 62-68, 07-2017.
    • Handle: RePEc:arp:ajoams:2017:p:62-68
    DOI: arpgweb.com/?ic=journal&journal=17&info=aims
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    References listed on IDEAS

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    1. Anguelov, Roumen & Lubuma, Jean M.-S., 2003. "Nonstandard finite difference method by nonlocal approximation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 465-475.
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