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A class of new Pouzet-Runge-Kutta-type methods for nonlinear functional integro-differential equations. (English) Zbl 1237.65146

Summary: 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.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G05 Singular nonlinear integral equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Software:

RODAS

References:

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