具有初始奇点的隐记变阶时间分式扩散方程的时序二阶方案

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI:10.1007/s10255-024-1054-2

Rui-lian Du, Zhi-zhong Sun

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引用次数: 0

摘要

在这项工作中，针对具有初始奇异性的隐含记忆变阶卡普托分数导数建立了一个新颖的时间步进（\overline{L1}\）公式。该公式可以获得二阶精度，并对误差估计进行了严格分析。作为应用，为隐记变阶时间分数扩散模型的初始边界值问题建立了完全离散差分方案。我们还提供了数值实验来支持我们的理论结果。

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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Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity

In this work, a novel time-stepping \(\overline{L1}\) formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity. This formula can obtain second-order accuracy and an error estimate is analyzed strictly. As an application, a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model. Numerical experiments are provided to support our theoretical results.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.