A fourth-order conservative difference scheme for the Riesz space-fractional Sine-Gordon equations and its fast implementation

Xing, Zhiyong; Wen, Liping; Hu, Xiao

doi:10.1016/j.apnum.2020.09.009

Cited by 11 publications

(2 citation statements)

References 37 publications

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“…Advances in Multimedia [15]. In this article, the unstructured grid method is used to store the multidimensional calculation units (control volume, surface, and node) of the structured grid into one dimension, and the unit needs to be expanded at the end to avoid the branch flow, as shown in Figure 2.…”

Section: Ways To Improve Parallel Efficiencymentioning

confidence: 99%

Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Zhan

2021

Advances in Multimedia

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In order to solve the numerical method of nonconservative ideal hydrodynamics equations, the viscous perturbation technique for solving nonconservative hydrodynamics equations is improved and tested by solving the Riemann problem. The calculation of nonconservative ideal fluid mechanics is based on the GRP format. This article aims at the calculation method of nonconservative ideal fluid mechanics in the GRP format. Riemann and the corresponding periodic vortex are processed. The multifluid network processing method in the article is compared with the current method. The result can prove that this format can be used to solve the nonconservative ideal fluid dynamics equation of multiple values in the GRP format group, its computing power is strong, and the result of the solution is accurate.

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Section: Ways To Improve Parallel Efficiencymentioning

confidence: 99%

Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Zhan

2021

Advances in Multimedia

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“…For instance, in mathematical modeling applications of a two-dimensional channel with porous walls, deformation of elastic beams, fluid dynamics. These problems have been studied by several mathematicians(see [11], [1], [4], [7], [2], [3], [8], [5], [15], [14] and the references therein. [11] converted the BVP to Initial Value Problem (IVP) and solved the linear equation while [13] solved the problem by transforming the fourth-order BVP to third-order BVP and applied by contracting mapping principle.…”

Section: Introductionmentioning

confidence: 99%

Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

Akgün

Rasulov

2021

Eur. J. Pure Appl. Math.

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

Sun,

Zhang,

Tang

2024

Numerical Linear Algebra App

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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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A fourth-order conservative difference scheme for the Riesz space-fractional Sine-Gordon equations and its fast implementation

Cited by 11 publications

References 37 publications

Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

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

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