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

Haiyan Yuan, Cheng Song and Peichen Wang

Mathematical Problems in Engineering, 2013, vol. 2013, 1-14

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 -stability, -stability, and the weak -stability on the basis of -algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:683137

DOI: 10.1155/2013/683137

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