Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system

Cai, Jiaxin; Wang, Yushun; Hua, Liu

doi:10.1016/j.jcp.2012.12.036

Cited by 46 publications

(20 citation statements)

References 21 publications

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“…Many numerical methods have been developed for CNLS equations, see [6][7][8][9][10][11] and references therein. In [7], some linear implicit schemes were presented for the initial-boundary value problem of CNLS system and proved the convergence of the difference solutions by von Neumann method.…”

Section: Proposition 1 If the Initial Valuesmentioning

confidence: 99%

“…This scheme is of second-order in time and fourth-order in space, however, noncompact. The space derivative operator u xx is discretized by (9). • Scheme V: to illustrate the necessity of compact scheme, we present the following existing noncompact scheme proposed by Wang et al in [22] as follows.…”

Section: Definition 1 a Matrix A Is Said To Be Circulant If It Can Bmentioning

confidence: 99%

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Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations

Kong

Hong

et al. 2015

Numerical Methods Partial

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In the manuscript, we present several numerical schemes to approximate the coupled nonlinear Schrödinger equations. Three of them are high-order compact and conservative, and the other two are noncompact but conservative. After some numerical analysis, we can find that the schemes are uniquely solvable and convergent. All of them are conservative and stable. By calculating the complexity, we can find that the compact schemes have the same computational cost with the noncompact ones. Numerical illustrations support our analysis. They verify that compact schemes are more efficient than noncompact ones from computation cost and accuracy.

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Section: Proposition 1 If the Initial Valuesmentioning

confidence: 99%

Section: Definition 1 a Matrix A Is Said To Be Circulant If It Can Bmentioning

confidence: 99%

Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations

Kong

Hong

et al. 2015

Numerical Methods Partial

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“…For the next few years, the theory of the local structure-preserving algorithm was used successfully for solving the PDEs (Refs. [23][24][25][26][27][28][29][30] and references therein), and the main advantage of the method is that it can keep the local structures of PDEs independent of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

Lang-yang

Tian

Cai

2020

Mathematical Problems in Engineering

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Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are Oh4+τ2. The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.

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“…Actually as the boundary conditions are periodic or homogeneous, the local energy-preserving/momentum-preserving schemes will be global energy-preserving/momentumpreserving schemes. On construction of the local structure-preserving schemes for some classical PDEs, we have done some works [15][16][17]. But there is no work on convergence analysis of these proposed local structure-preserving schemes.…”

Section: Introductionmentioning

confidence: 99%

Local energy‐ and momentum‐preserving schemes for Klein‐Gordon‐Schrödinger equations and convergence analysis

Cai

Hong²,

Wang

2017

Numerical Methods Partial

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In this article, we obtain local energy and momentum conservation laws for the Klein-Gordon-Schrödinger equations, which are independent of the boundary condition and more essential than the global conservation laws. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose local energy-and momentum-preserving schemes for the equations. The merit of the proposed schemes is that the local energy/momentum conservation law is conserved exactly in any time-space region. With suitable boundary conditions, the schemes will be charge-and energy-/momentumpreserving. Nonlinear analysis shows LEP schemes are unconditionally stable and the numerical solutions converge to the exact solutions with order O(τ 2 + h 2 ). The theoretical properties are verified by numerical experiments.

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Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system

Cited by 46 publications

References 21 publications

Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations

Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations

Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

Local energy‐ and momentum‐preserving schemes for Klein‐Gordon‐Schrödinger equations and convergence analysis

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