A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations | Zendy

Chengjian Zhang | Zendy

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A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations

Author(s) -

Chengjian Zhang

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/642318

Subject(s) - mathematics , runge–kutta methods , lipschitz continuity , nonlinear system , class (philosophy) , stability (learning theory) , mathematical analysis , type (biology) , differential equation , numerical analysis , computer science , ecology , physics , quantum mechanics , artificial intelligence , machine learning , biology

This paper presents a class of new numerical methods for nonlinear functional-integrodifferential equations, which are derived by an adaptation of Pouzet-Runge-Kutta methods originally introduced for standard Volterra integrodifferential equations. Based on the nonclassical Lipschitz condition, analytical and numerical stability is studied and some novel stability criteria are obtained. Numerical experiments further illustrate the theoretical results and the effectiveness of the methods. In the end, a comparison between the presented methods and the existed related methods is given

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