Burgers方程数值解的多重二次拟插值格式

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.09.025

JiHong Zhang, JiaLi Yu

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引用次数: 0

摘要

Multi-Quadrics （MQ）径向基函数（RBF）拟插值由于其简单方便，避免了插值点多时可能出现的病态问题，并且能够直接提供数值逼近结果而受到广泛关注。本文提出了一种新的离散数据拟插值LN，并证明了它具有线性再现性和较高的计算精度，并且不需要在两个端点处的一阶导数值，使其更易于使用。最后，给出了求解Burgers方程的数值格式，并进行了数值实验，并与其他方法进行了比较。数值结果验证了该拟插值器LN的有效性和准确性。

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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A Multi-Quadrics quasi-interpolation scheme for numerical solution of Burgers' equation

The Multi-Quadrics (MQ) radial basis function (RBF) quasi-interpolant has received widespread attention due to its simplicity and convenience, avoiding the possible ill-conditioning problem that may occur if there are a lot of interpolation points, and being able to directly provide numerical approximation results. We present a new quasi-interpolant

L_{N}

for scattered data and prove that it has the property of linear reproducing and high computational accuracy, and does not require the first derivative values at the two endpoints, making it easier to use. Finally, the numerical scheme for solving Burgers’ equation is presented, and numerical experiments are carried out and compared with other methods. The numerical results verify the effectiveness and accuracy of the new quasi-interpolant

L_{N}

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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.