Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations

Shi, Wei; Wu, Xinyuan; Xia, Jianlin

doi:10.1016/j.jcp.2012.07.004

Cited by 35 publications

(2 citation statements)

References 36 publications

(52 reference statements)

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“…In the last few decades, various structure-preserving methods have been developed for solving the NKGE (2.1), including symplectic methods ( e.g., see [9,22,24]), multisymplectic methods (e.g., see [17,26,30,37]) and energy-preserving methods (e.g., see [1,6,12,31]), local momentum-preserving methods (e.g., see [19,32]), etc. However, there has been no reference considering a linearly implicit structure-preserving exponential scheme for the NKGE (2.1) to our knowledge.…”

Section: Reformation Of the Model Equation Through The Sav Approachmentioning

confidence: 99%

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

Jiang,

Wang,

Cai

2019

Preprint

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In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea of the scalar auxiliary variable approach. Comparing with the original exponential energy-preserving integrator which usually leads to a nonlinear algebraic system, our new method only involve a linear system with constant coefficient matrix. Taking the nonlinear Klein-Gordon equation for example, we derive the concrete energy-preserving scheme and demonstrate its high efficiency through numerical experiments.

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Section: Reformation Of the Model Equation Through The Sav Approachmentioning

confidence: 99%

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

Jiang,

Wang,

Cai

2019

Preprint

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“…The implicit-explicit combination of Crank-Nicolson and LF schemes, frequently used in atmosphere, ocean, and climate codes, is studied in [11]. Some extensions of LF methods are presented in [27].…”

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confidence: 99%

Leap-frog method for stochastic functional wave equations

Leszczyński¹,

Matusik²,

Wrzosek³

2020

etna

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We perform a time-space discretisation, known as the leapfrog method, for nonlinear stochastic functional wave equations driven by multiplicative time-space white noise. To prove its stability we apply Cairoli's maximal inequalities for two-parameter martingales and provide a lemma for estimating solutions to a class of stochastic wave equations and a Gronwall-type inequality over cones. The method converges in L 2 at a rate of O(√ h), where h is a time-space step size.

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Extended Leap-Frog Methods for Hamiltonian Wave Equations

You

Wang

2013

Structure-Preserving Algorithms for Oscillatory Differential Equations

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Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations

Cited by 35 publications

References 36 publications

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

Leap-frog method for stochastic functional wave equations

Extended Leap-Frog Methods for Hamiltonian Wave Equations

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