Fractal cubic multiquadric quasi-interpolation

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-27 DOI:10.1016/j.cam.2025.117099

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

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引用次数: 0

Abstract

In this article, we propose a novel class of fractal cubic multiquadric functions that generalize the classical cubic multiquadric functions. By employing these fractal multiquadric functions, we develop a fractal quasi-interpolation operator, denoted by

L_{d}^{α}

. We examine various properties of these fractal cubic multiquadric approximants, such as shape-preserving characteristics and the ability to reproduce quadratic polynomials. Error estimates for these approximants are also derived, and estimates for the box-dimension of the graphs of fractal cubic multiquadric approximants are given. Numerical examples are presented to validate these theoretical findings and highlight the benefits of the fractal quasi-interpolant

L_{d}^{α} f

. Additionally, we apply the proposed fractal quasi-interpolants to solve an integral equation with a non-smooth degenerate kernel. This approach shows a high rate of convergence to the exact solution. Box-dimension results for the numerical solution of this integral equation are also established.

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分形三次多次拟插值

在本文中，我们提出了一类新的分形三次多重函数，它推广了经典三次多重函数。利用这些分形多重二次函数，我们得到了一个分形拟插值算子，用Ldα表示。我们研究了这些分形三次多次近似的各种性质，如形状保持特征和再现二次多项式的能力。给出了这些近似的误差估计，并给出了分形三次多次近似图的盒维估计。数值算例验证了这些理论发现，并强调了分形拟插值Ldαf的优点。此外，我们应用所提出的分形拟插值来求解具有非光滑退化核的积分方程。这种方法对精确解有很高的收敛速度。建立了该积分方程数值解的盒维结果。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.