A novel attempt for finding comparatively accurate solution for sine‐Gordon equation comprising Riesz space fractional derivative

Gupta, A. K.; Ray, S. Saha

doi:10.1002/mma.3736

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…Recently, this equation has been largely studied and many significant achievements have been made in Refs. [7,8,10].…”

Section: Introductionmentioning

confidence: 99%

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A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

Cai

Wang

2019

Preprint

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This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on the newly developed invariant energy quadratization method. First, we reformulate the equation as a canonical Hamiltonian system by virtue of the variational derivative of the functional with fractional Laplacian. Then, we utilize the fractional centered difference formula to discrete the equivalent system derived by the invariant energy quadratization method in space direction, and obtain a conservative semidiscrete scheme. Subsequently, the linearly implicit structure-preserving method is applied for the resulting semi-discrete system to arrive at a fully-discrete conservative scheme. The stability, solvability and convergence in the maximum norm of the numerical scheme are given. Furthermore, a fast algorithm based on the fast Fourier transformation technique is used to reduce the computational complexity in practical computation. Finally, numerical examples are provided to confirm our theoretical analysis results.

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“…Recently, this equation has been largely studied and many significant achievements have been made in Refs. [7,8,10].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, a slice of researchers have devoted great energy to discuss the computation for the FSG equation, and the readers can refer to Refs. [7,9,10] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

Cai

Wang

2019

Preprint

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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 linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

Cai

Wang

2021

Applied Numerical Mathematics

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A novel attempt for finding comparatively accurate solution for sine‐Gordon equation comprising Riesz space fractional derivative

Cited by 5 publications

References 20 publications

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

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

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

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