基于样条Riesz小波的非线性多项分数阶微分方程数值解

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-02-13 DOI:10.1016/j.amc.2025.129359

Wei Tang, Da Xu

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引用次数: 0

摘要

本文提出了一种直接求解多项分数阶微分方程数值解的方法。该方法基于将原方程转化为多阶分数阶方程的等效系统。该系统采用Riesz样条小波的分数阶导数和配点法进行离散化。然后将原问题转化为一个代数方程组，可以很容易地求解。最后，通过数值算例和与其他方法的比较，验证了该方法的有效性和准确性。

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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Numerical solution of nonlinear multi-term fractional differential equations based on spline Riesz wavelets

In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.