时间分数阶电报方程的稳定收敛杂化不连续伽辽金方法

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED Numerical Functional Analysis and Optimization Pub Date : 2023-07-26 DOI:10.1080/01630563.2023.2236690

Sh. Baharlouei, R. Mokhtari

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引用次数: 0

摘要

摘要本文推广了杂交不连续伽辽金（HDG）方法在求解时间分数电报方程中的应用。事实上，我们使用HDG方法进行空间离散化，使用L1和L2有限差分格式使用非均匀网格进行时间离散化。由于一类特殊的离散Gronwall不等式，我们证明了HDG方法是无条件稳定的，并且它是以最优空间收敛阶收敛的。通过两个数值实验验证了理论结果。

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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A Stable and Convergent Hybridized Discontinuous Galerkin Method for Time-Fractional Telegraph Equations

Abstract In this paper, we extend the application of the hybridized discontinuous Galerkin (HDG) method to solve time-fractional telegraph equations. In fact, we use an HDG method for space discretization and L1 and L2 finite difference schemes using non-uniform meshes for time discretization. Thanks to a special kind of discrete Gronwall inequality, we prove that the HDG method is unconditionally stable and it is convergent with the optimal spatial order of convergence. Two numerical experiments are tested to confirm the theoretical results.

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.