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

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。

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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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