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

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 (k,l)-algebraically stable and asymptotically stable are introduced; then the asymptotic...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.714-726-869
Hauptverfasser: Yuan, Haiyan, Song, Cheng
Format: Artikel
Sprache:eng
Schlagworte:
Convergence (Mathematics)
Differential equations, Nonlinear
Integral equations
Mathematical research
Methods
Nonlinear programming
Numerical analysis
Studies
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Zusammenfassung: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
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/679075