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Wang, Wan-Sheng; Zhang, Yuan; Li, Shou-Fu

Nonlinear stability of one-leg methods for delay differential equations of neutral type. (English) Zbl 1137.65052

Appl. Numer. Math. 58, No. 2, 122-130 (2008).
The paper explores one-leg methods for neutral delay differential equations and considers aspects of stability. New stability concepts (GS-, GAS- and weak GS-stablility) are introduced and results are given that relate these concepts to already known concepts such as A-stability.
The paper is structured as follows. There is a preliminary section that provides an introduction and background information, followed by a section that defines the problem class, and an introduction to the numerical methods to be considered. The main sections of the paper are a section giving stability theory, and a section giving the results of some numerical experiments.
Reviewer: Neville Ford (Chester)

Cited in 32 Documents

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K40 Neutral functional-differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Keywords:

neutral delay differential equations; nonlinear stability; one-leg methods; numerical experiments
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Full Text: DOI

References:

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