Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations. (23rd May 2013)

• Record Type: Journal Article
• Authors: Yuan, Haiyan; Song, Cheng; Wang, Peichen
• Other Names: Karimi Hamid Reza Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-05-23
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/683137
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss the GR ( l ) -stability, GAR ( l ) -stability, and the weak GAR ( l ) -stability on the basis of ( k, l ) -algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.