, Volume 90, Issue 1-2, pp 57-71
Date: 15 Jul 2010

The extended Pouzet–Runge–Kutta methods for nonlinear neutral delay-integro-differential equations

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Abstract

This paper deals with the extended Pouzet–Runge–Kutta methods for nonlinear neutral delay-integro-differential equations. Nonlinear stability and numerical implementation of the methods are investigated. It is proven under the suitable conditions that the extended Pouzet–Runge–Kutta methods are globally and asymptotically stable for problems of the class \({\mathbb{NRI}{(\alpha,\beta,\gamma,\nu)}}\). Numerical examples further illustrate the theoretical results and the methods’ effectiveness.