2020
DOI: 10.1016/j.apnum.2019.12.016
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Abstract: In this paper, we develop a novel class of arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation. With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system with a quadratic energy functional, which inherits a modified energy conservation law. The new system are then discretized by the standard Fourier pseudo-spectral method, which can exactly preserve the semi-discrete energy conservation law. Subsequently, t… Show more

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Cited by 30 publications
(8 citation statements)
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“…In this section, we propose a class of high-order energy-preserving schemes for the equation (1.1). Inspired by [9,17], we first shall introduce appropriate quadratic auxiliary variables to reformulate the Hamiltonian energy into a quadratic form. For clarity, we take p = 2, 3 and 5 as examples to expound this procedure, as follows:…”
Section: High-order Energy-preserving Schemementioning
confidence: 99%
“…In this section, we propose a class of high-order energy-preserving schemes for the equation (1.1). Inspired by [9,17], we first shall introduce appropriate quadratic auxiliary variables to reformulate the Hamiltonian energy into a quadratic form. For clarity, we take p = 2, 3 and 5 as examples to expound this procedure, as follows:…”
Section: High-order Energy-preserving Schemementioning
confidence: 99%
“…In this section, we propose a class of temporal high-order linear semi-discrete energypreserving schemes for the RLW equation (1.1) by using the EQ approach [17,26,49,51] and the similar linearized idea mentioned as above. To this end, we start with introducing an auxiliary variable…”
Section: High-order Linear Energy-preserving Schemementioning
confidence: 99%
“…Especially, the term "quadratic auxiliary variable (QAV) approach" was coined by Gong et al in [21]. The QAV approach is a special subclass of the IEQ approach and the key differences between them are: (i) the auxiliary variable introduced by the QAV approach shall be quadratic; (ii) when a high-order accurate method in time which can preserve the quadratic invariant is applied to the equivalent system, the resulting method can preserve both the quadratic invariant and the original Hamiltonian energy [21,22] instead of a modified energy [17,30]. Thus, the QAV approach will be an efficient strategy to develop high-order accurate mass-and energy-preserving scheme for the QZS (1.1), however to our knowledge, there has been no reference considering this issue.…”
Section: Introductionmentioning
confidence: 99%