## Abstract and Applied Analysis

### Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations

#### Abstract

This paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments ${u}^{\prime }\mathbf{\left(}t\mathbf{\right)} \mathbf{=} au\mathbf{\left(}t\mathbf{\right)} \mathbf{+} bu\mathbf{\left(}\mathbf{\left[}t\mathbf{\right]}\mathbf{\right)}$. The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the conditions of oscillation for the Euler-Maclaurin method are obtained. We prove that the Euler-Maclaurin method preserves the oscillations of the analytic solution. Moreover, the relationships between stability and oscillations are discussed for analytic solution and numerical solution, respectively. Finally, some numerical experiments for verifying the theoretical analysis are also provided.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 232484, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511883

Digital Object Identifier
doi:10.1155/2013/232484

Mathematical Reviews number (MathSciNet)
MR3055930

Zentralblatt MATH identifier
1275.65037

#### Citation

Wang, Qi; Wen, Jiechang; Qiu, Shenshan. Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations. Abstr. Appl. Anal. 2013 (2013), Article ID 232484, 9 pages. doi:10.1155/2013/232484. https://projecteuclid.org/euclid.aaa/1393511883

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