具有高频外在振荡的线性中立型时滞微分方程的渐近数值解

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-09-20 DOI:10.1051/m2an/2022075

M. Kzaz, Fatna Maach

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引用次数: 4

摘要

给出了一种求解具有高振荡强迫项的线性中立型时滞微分方程的高效简便方法。该方法基于摄动振荡参数逆幂的渐近展开式。渐近展开式的每一项都是由递归导出的。计算的代价基本上与振荡参数无关。给出了数值算例，结果表明，用较少的渐近展开项，解的逼近精度较高。

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Asymptotic-numerical solvers for linear neutral delay differential equations with high- frequency extrinsic oscillations

We present a method to compute efficiently and easily solutions of systems of linear neutral delay differential equations with highly oscillatory forcing terms. This method is based on asymptotic expansions in inverse powers of a perturbed oscillatory parameter. Each term of the asymptotic expansion is derived by recursion. The cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided and show that with few terms of the asymptotic expansion, the solutions are approximated with high accuracy.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.