半线性子扩散方程分级网格上的 L2 型方法误差分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-10 DOI:10.1016/j.aml.2024.109306

Natalia Kopteva

引用次数: 0

摘要

我们考虑了一个具有分数阶 α∈(0,1) 的卡普托时间导数的半线性初始边界值问题，其解通常在初始时间表现出奇异行为。对于阶数为 3-α 的 L2- 型离散化，我们给出了具有任意分级程度的分级时间网格上的尖锐时间点误差边界。

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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Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

A semilinear initial–boundary value problem with a Caputo time derivative of fractional order $α \in (0, 1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order $3 - α$ , we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.

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来源期刊

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.