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Volume 42, Issue 3
One-Parameter Finite Difference Methods and Their Accelerated Schemes for Space-Fractional Sine-Gordon Equations with Distributed Delay

Tao Sun, Chengjian Zhang & Haiwei Sun

DOI: 10.4208/jcm.2206-m2021-0240

J. Comp. Math., 42 (2024), pp. 705-734.

Published online: 2024-04

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  • Abstract

This paper deals with numerical methods for solving one-dimensional (1D) and two-dimensional (2D) initial-boundary value problems (IBVPs) of space-fractional sine-Gordon equations (SGEs) with distributed delay. For 1D problems, we construct a kind of one-parameter finite difference (OPFD) method. It is shown that, under a suitable condition, the proposed method is convergent with second order accuracy both in time and space. In implementation, the preconditioned conjugate gradient (PCG) method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method. For 2D problems, we develop another kind of OPFD method. For such a method, two classes of accelerated schemes are suggested, one is alternative direction implicit (ADI) scheme and the other is ADI-PCG scheme. In particular, we prove that ADI scheme can arrive at second-order accuracy in time and space. With some numerical experiments, the computational effectiveness and accuracy of the methods are further verified. Moreover, for the suggested methods, a numerical comparison in computational efficiency is presented.

  • Keywords

Fractional sine-Gordon equation with distributed delay, One-parameter finite difference methods, Convergence analysis, ADI scheme, PCG method.

  • AMS Subject Headings

65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-705, author = {Sun , TaoZhang , Chengjian and Sun , Haiwei}, title = {One-Parameter Finite Difference Methods and Their Accelerated Schemes for Space-Fractional Sine-Gordon Equations with Distributed Delay}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {3}, pages = {705--734}, abstract = {

This paper deals with numerical methods for solving one-dimensional (1D) and two-dimensional (2D) initial-boundary value problems (IBVPs) of space-fractional sine-Gordon equations (SGEs) with distributed delay. For 1D problems, we construct a kind of one-parameter finite difference (OPFD) method. It is shown that, under a suitable condition, the proposed method is convergent with second order accuracy both in time and space. In implementation, the preconditioned conjugate gradient (PCG) method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method. For 2D problems, we develop another kind of OPFD method. For such a method, two classes of accelerated schemes are suggested, one is alternative direction implicit (ADI) scheme and the other is ADI-PCG scheme. In particular, we prove that ADI scheme can arrive at second-order accuracy in time and space. With some numerical experiments, the computational effectiveness and accuracy of the methods are further verified. Moreover, for the suggested methods, a numerical comparison in computational efficiency is presented.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2206-m2021-0240}, url = {http://global-sci.org/intro/article_detail/jcm/23033.html} }
TY - JOUR T1 - One-Parameter Finite Difference Methods and Their Accelerated Schemes for Space-Fractional Sine-Gordon Equations with Distributed Delay AU - Sun , Tao AU - Zhang , Chengjian AU - Sun , Haiwei JO - Journal of Computational Mathematics VL - 3 SP - 705 EP - 734 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2206-m2021-0240 UR - https://global-sci.org/intro/article_detail/jcm/23033.html KW - Fractional sine-Gordon equation with distributed delay, One-parameter finite difference methods, Convergence analysis, ADI scheme, PCG method. AB -

This paper deals with numerical methods for solving one-dimensional (1D) and two-dimensional (2D) initial-boundary value problems (IBVPs) of space-fractional sine-Gordon equations (SGEs) with distributed delay. For 1D problems, we construct a kind of one-parameter finite difference (OPFD) method. It is shown that, under a suitable condition, the proposed method is convergent with second order accuracy both in time and space. In implementation, the preconditioned conjugate gradient (PCG) method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method. For 2D problems, we develop another kind of OPFD method. For such a method, two classes of accelerated schemes are suggested, one is alternative direction implicit (ADI) scheme and the other is ADI-PCG scheme. In particular, we prove that ADI scheme can arrive at second-order accuracy in time and space. With some numerical experiments, the computational effectiveness and accuracy of the methods are further verified. Moreover, for the suggested methods, a numerical comparison in computational efficiency is presented.

Sun , TaoZhang , Chengjian and Sun , Haiwei. (2024). One-Parameter Finite Difference Methods and Their Accelerated Schemes for Space-Fractional Sine-Gordon Equations with Distributed Delay. Journal of Computational Mathematics. 42 (3). 705-734. doi:10.4208/jcm.2206-m2021-0240
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