Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

Haiyan Yuan and Cheng Song

Abstract and Applied Analysis, 2013, vol. 2013, 1-13

Abstract:

This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of -algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a -algebraically stable two-step Runge-Kutta method with is proved. For the convergence, the concepts of -convergence, diagonally stable, and generalized stage order are firstly introduced; then it is proved by some theorems that if a two-step Runge-Kutta method is algebraically stable and diagonally stable and its generalized stage order is , then the method with compound quadrature formula is -convergent of order at least , where depends on the compound quadrature formula.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2013/679075.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2013/679075.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:679075

DOI: 10.1155/2013/679075

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().