Article

Computing

, Volume 90, Issue 1, pp 57-71

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

  • Chengjian ZhangAffiliated withSchool of Mathematics and Statistics, Huazhong University of Science and Technology
  • , Tingting QinAffiliated withSchool of Mathematics and Statistics, Huazhong University of Science and Technology Email author 
  • , Jie JinAffiliated withSchool of Mathematics and Statistics, Huazhong University of Science and Technology

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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.

Keywords

Neutral delay-integro-differential equations Nonlinear stability Pouzet–Runge–Kutta methods

Mathematics Subject Classification (2000)

65L20 65L06 65R20