微分方程解的切比雪夫三角洲形和切比雪夫伪谱方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-04-06 DOI:10.1016/j.matcom.2025.03.034

Fahir Talay Akyildiz , Kuppalapalle Vajravelu , Cemil Tunç , John Abraham

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引用次数: 0

摘要

本文介绍了一种新的切比雪夫三角函数（CDSF），并建立了它与插值问题中切比雪夫多项式的关系。我们首先证明 CDSF 确实是哈尔空间的一个基。然后，我们推导出选择合适配准点的条件。接下来，我们介绍并开发了切比雪夫三角型伪谱方法。提出了切比雪夫伪谱法的离散 L2 准则和索波列夫准则 Hp 的误差边界。介绍了泊松方程、泊松-玻尔兹曼方程和斯托克斯第二问题近似解的测试，以及使用以下方法预测结果的比较：1.切比雪夫伪谱法；2.余弦-△形伪谱法；3.余弦-伪谱法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Chebyshev delta shaped and Chebyshev pseudo-spectral methods for solutions of differential equations

In this paper we introduce a new Chebyshev delta-shaped function (CDSF) and establish its relationship with Chebyshev polynomials in interpolation problems. We first prove that CDSF is indeed form a basis for a Haar space. We then derive the conditions for the selection of suitable collocation points. Next, we introduce and develop Chebyshev delta-shaped pseudo-spectral method. Error bounds on discrete

L_{2} -

norm and Sobolev norm

(H^{p})

are presented for the Chebyshev pseudo-spectral method. Tests to find approximate solutions for the Poisson, Poisson-Boltzmann equations and Stokes second problem and comparisons of the predictions using the following methods are presented:

1.
Chebyshev pseudo-spectral method,
2.
Cosine-sine delta-shaped pseudo-spectral method, and
3.
Cosine-sine pseudo-spectral method.

Excellent convergent and stable results are obtained by using our newly defined Chebyshev delta-shaped basis functions and this is documented for the first time.

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.