多步赫尔墨特-伯克霍夫预测器-校正器方案

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-07-31 DOI:10.1016/j.apnum.2024.07.011

Arjun Thenery Manikantan, Jochen Schütz

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引用次数: 0

摘要

在本研究中，我们引入了一种多步多衍生预测器-校正器时间积分方案，类似于 Schütz 等人（2022 年）的方案，并结合了多步正交规则。我们进行了高达八阶的稳定性分析，并对方案进行了优化，以实现大......时的稳定性。我们对表现出不同刚度条件的常微分方程以及表现出非线性和高阶项的偏微分方程进行了数值实验。结果表明，所提出的方案在各种情况下都具有收敛性和灵活性。

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Multi-step Hermite-Birkhoff predictor-corrector schemes

In this study, we introduce a multi-step multi-derivative predictor-corrector time integration scheme analogous to the schemes in Schütz et al. (2022) [13], incorporating a multi-step quadrature rule. We conduct stability analysis up to order eight and optimize the schemes to achieve $A (α)$ -stability for large α. Numerical experiments are performed on ordinary differential equations exhibiting diverse stiffness conditions, as well as on partial differential equations showcasing non-linearity and higher-order terms. Results demonstrate the convergence and flexibility of the proposed schemes across diverse situations.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.