Performance of Ritz-Piecewise Gegenbauer Approach for Two Types of Fractional Pantograph Equations Including Piecewise Fractional Derivative

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-05 DOI:10.1002/mma.10724

Haniye Dehestani

引用次数: 0

Abstract

This paper introduces a novel numerical algorithm for solving pantograph differential equations and Volterra functional integro-differential equations including the piecewise fractional derivative. The proposed algorithm combines the piecewise Gegenbauer functions, the Ritz method, and operational matrices. These functions have great flexibility to match the problems containing piecewise fractional derivatives. Due to the problems, we calculate the operational matrix of derivatives, the operational matrix of the piecewise fractional derivative, and the pantograph operational matrix. By employing the proposed numerical algorithm, we transform the problems into a system of algebraic equations. Moreover, we discuss the error estimation of the approximate solution and residual error. Finally, we provide details on the implementation of this technique through several numerical examples to demonstrate its applicability.

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本文介绍了一种求解受电弓微分方程和 Volterra 函数积分微分方程（包括分片导数）的新型数值算法。所提出的算法结合了片断 Gegenbauer 函数、Ritz 方法和运算矩阵。这些函数具有极大的灵活性，可以与包含分式导数的问题相匹配。由于问题的存在，我们计算了导数运算矩阵、分片导数运算矩阵和受电弓运算矩阵。通过采用所提出的数值算法，我们将问题转化为代数方程系统。此外，我们还讨论了近似解的误差估计和残余误差。最后，我们通过几个数值示例详细介绍了该技术的实施，以证明其适用性。

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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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.