基于诺依曼数列的高振荡微分方程数值积分器

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED
Rafał Perczyński, Grzegorz Madejski
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引用次数: 0

摘要

我们提出了一种基于诺依曼数列和费伦正交的三阶数值积分器,主要针对高度振荡的偏微分方程。该方法可用于表现出小幅或中幅振荡的方程;然而,与直觉相反,大幅振荡会提高方案的精度。利用所提出的方法,该方法的收敛阶数很容易得到改善。我们还对该方法进行了误差分析。我们考虑了涉及一阶导数和二阶导数的线性演化方程,这些方程以椭圆微分算子为特征,例如热方程或波方程。数值实验考虑了空间维度大于 1 的情况,证实了理论研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Numerical integrator for highly oscillatory differential equations based on the Neumann series

Numerical integrator for highly oscillatory differential equations based on the Neumann series

We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate oscillations; however, counter-intuitively, large oscillations increase the accuracy of the scheme. With the proposed approach, the convergence order of the method can be easily improved. Error analysis of the method is also performed. We consider linear evolution equations involving first- and second-time derivatives that feature elliptic differential operators, such as the heat equation or the wave equation. Numerical experiments consider the case in which the space dimension is greater than one and confirm the theoretical study.

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来源期刊
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
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