Fractal Multiquadric Interpolation Functions

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-10-18 DOI:10.1137/23m1578917

D. Kumar, A. K. B. Chand, P. R. Massopust

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2349-2369, October 2024.
Abstract. In this article, we impose fractal features onto classical multiquadric (MQ) functions. This generates a novel class of fractal functions, called fractal MQ functions, where the symmetry of the original MQ function with respect to the origin is maintained. This construction requires a suitable extension of the domain and similar partitions on the left side with the same choice of scaling parameters. Smooth fractal MQ functions are proposed to solve initial value problems via a collocation method. Our numerical computations suggest that fractal MQ functions offer higher accuracy and more flexibility for the solutions compared to the existing classical MQ functions. Some approximation results associated with fractal MQ functions are also presented.

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分形多四边形插值函数

SIAM 数值分析期刊》第 62 卷第 5 期第 2349-2369 页，2024 年 10 月。摘要在这篇文章中，我们将分形特征强加给经典多曲函数（MQ）。这就产生了一类新的分形函数，称为分形 MQ 函数，其中保持了原始 MQ 函数相对于原点的对称性。这种构造需要对域进行适当扩展，并在左侧进行类似的分区，同时选择相同的缩放参数。我们提出了平滑分形 MQ 函数，以通过搭配法解决初值问题。我们的数值计算表明，与现有的经典 MQ 函数相比，分形 MQ 函数提供了更高的精度和更灵活的解决方案。此外，还介绍了与分形 MQ 函数相关的一些近似结果。

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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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.