A double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED Applied Mathematics Letters Pub Date : 2024-11-21 DOI:10.1016/j.aml.2024.109388
Zhihao Sheng , Yang Liu , Yonghai Li
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Abstract

In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter θ and a new variable parameter δ. We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.
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双参数移位卷积正交公式及其在分数移动/不移动传输方程中的应用
本文提出了一种新的二阶移位卷积正交(SCQ)公式,包括移位参数θ和新的可变参数δ。我们证明了时间分数导数新公式的二阶截断误差,并推导出公式权重的非负属性。将新公式与有限元法相结合,我们开发了分数移动/非移动传输方程的高阶数值方案。此外,我们还分析了数值方法的稳定性和误差估计。我们提出了数值测试来进一步验证我们的理论结果。
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
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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