Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 679075, 13 pages.
Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations
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.
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 679075, 13 pages.
First available in Project Euclid: 26 February 2014
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Yuan, Haiyan; Song, Cheng. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 679075, 13 pages. doi:10.1155/2013/679075. https://projecteuclid.org/euclid.aaa/1393444389