On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods

IF 0.6 3区 数学 Q3 MATHEMATICS Periodica Mathematica Hungarica Pub Date : 2023-11-23 DOI:10.1007/s10998-023-00557-y
Teshome Bayleyegn, István Faragó, Ágnes Havasi
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Abstract

The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes h and h/2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from p to \(p+2\), and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked.

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结合显式龙格-库塔方法的多重Richardson外推的收敛性
任何微分方程系统的收敛时间积分方法的精度阶数都可以通过使用称为理查德森外推的序列加速方法及其变体(经典理查德森外推和多重理查德森外推)来提高。理查德森外推的原始(经典)版本包括采用由两个不同的时间步长(时间步长为h和h/2)通过相同的数值方法获得的数值解的线性组合。多重理查德森外推是这一过程的推广,其中外推应用于一些基础数值方法和经典理查德森外推的结合。此过程将基础方法的精度顺序从p增加到\(p+2\),并且每次重复,顺序进一步增加1。本文研究了基于显式龙格-库塔方法的多重Richardson外推的收敛性,并对其计算效率进行了检验。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.
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