A high order predictor-corrector method with non-uniform meshes for fractional differential equations

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-12 DOI:10.1007/s13540-024-00303-2

Farzaneh Mokhtarnezhadazar

引用次数: 0

Abstract

This article proposes a predictor-corrector scheme for solving the fractional differential equations \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\) with non-uniform meshes. We reduce the fractional differential equation into the Volterra integral equation. Detailed error analysis and stability analysis are investigated. The convergent order of this method on non-uniform meshes is still 3 though \({}_0^C D_t^\alpha y(t)\) is not smooth at \(t=0\). Numerical examples are carried out to verify the theoretical analysis.

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分数微分方程的非均匀网格高阶预测器-校正器方法

本文提出了一种预测器-校正器方案，用于求解非均匀网格的分数微分方程 \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\)。我们将分数微分方程简化为 Volterra 积分方程。研究了详细的误差分析和稳定性分析。虽然 \({}_0^C D_t^\alpha y(t)\) 在 \(t=0\) 时并不平滑，但该方法在非均匀网格上的收敛阶数仍为 3。为了验证理论分析，我们进行了数值示例。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.