Accelerated schemes of compact difference methods for space-fractional sine-Gordon equations with distributed delay

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-04-16 DOI:10.1002/nla.2556

Tao Sun, Chengjian Zhang, Changyang Tang

引用次数: 0

Abstract

In this paper, for quickly solving one- and two-dimensional space-fractional sine-Gordon equations with distributed delay, we suggest several accelerated schemes of direct compact difference (DCD) methods. For one-dimensional (1D) problems, with a function transformation, we construct an indirect compact difference (ICD) method, which requires less calculation cost than the corresponding DCD method, and prove under the appropriate conditions that ICD method has second-order (resp. forth-order) calculation accuracy in time (resp. space). By extending the argument for 1D case, we further obtain an ICD method for solving two-dimensional (2D) problems and derive the similar convergence result. For ICD and DCD methods of 2D problems, we also give their alternative direction implicit (ADI) schemes. Moreover, for the fast implementations of ICD method of 1D problems and indirect ADI method of 2D problems, we further present their acceleration strategies. Finally, with a series of numerical experiments, the findings in this paper are further confirmed.

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具有分布式延迟的空间分数正弦-戈登方程的紧凑差分法加速方案

在本文中，为了快速求解具有分布延迟的一维和二维空间分数正弦-戈登方程，我们提出了几种直接紧凑差分（DCD）方法的加速方案。对于有函数变换的一维（1D）问题，我们构建了一种间接紧凑差分（ICD）方法，它比相应的直接紧凑差分方法需要更少的计算成本，并在适当条件下证明了 ICD 方法在时间（或空间）上具有二阶（或四阶）计算精度。通过扩展对一维情况的论证，我们进一步得到了求解二维（2D）问题的 ICD 方法，并推导出类似的收敛结果。对于二维问题的 ICD 和 DCD 方法，我们还给出了它们的替代方向隐式（ADI）方案。此外，对于一维问题的 ICD 方法和二维问题的间接 ADI 方法的快速实现，我们进一步介绍了它们的加速策略。最后，通过一系列数值实验，我们进一步证实了本文的结论。

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

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.