Computing

, Volume 90, Issue 1, pp 57–71

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

Authors

  • Chengjian Zhang
    • School of Mathematics and StatisticsHuazhong University of Science and Technology
    • School of Mathematics and StatisticsHuazhong University of Science and Technology
  • Jie Jin
    • School of Mathematics and StatisticsHuazhong University of Science and Technology
Article

DOI: 10.1007/s00607-010-0103-2

Cite this article as:
Zhang, C., Qin, T. & Jin, J. Computing (2010) 90: 57. doi:10.1007/s00607-010-0103-2

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 equationsNonlinear stabilityPouzet–Runge–Kutta methods

Mathematics Subject Classification (2000)

65L2065L0665R20

Copyright information

© Springer-Verlag 2010