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Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-19
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 (k,l)-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l)-algebraically stable two-step Runge-Kutta method with 0 For the convergence, the concepts of D-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 p, then the method with compound quadrature formula is D-convergent of order at least min{p,ν}, where ν depends on the compound quadrature formula.
American Psychological Association (APA)
Yuan, Haiyan& Song, Cheng. 2013. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-489827
Modern Language Association (MLA)
Yuan, Haiyan& Song, Cheng. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations. Abstract and Applied Analysis No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-489827
American Medical Association (AMA)
Yuan, Haiyan& Song, Cheng. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-489827
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-489827