非线性哈密顿系统的有效标量辅助变量（SAV）谱Petrov-Galerkin近似

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-10-03 DOI:10.1016/j.cam.2025.117127

Jing An , Waixiang Cao , Zhimin Zhang

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引用次数: 0

摘要

针对非线性哈密顿系统，提出并研究了一种新的标量辅助变量谱Petrov-Galerkin近似。该算法是在SAV方法和谱Petrov-Galerkin （SPG）方法的基础上建立起来的，它同时具有SAV方法和SPG方法的能量守恒性和高阶精度等优点。严格的理论分析表明，所提出的算法是适定的和收敛的。进一步研究了其守恒性质。特别是，我们证明了SAV-SPG方法准确地保留了修正后的能量，并在一定的谱精度下保持了辛结构。数值实验验证了算法的有效性。

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An efficient scalar auxiliary variable (SAV) spectral Petrov–Galerkin approximation for nonlinear Hamiltonian systems

In this paper, a new scalar auxiliary variable (SAV) spectral Petrov–Galerkin approximation is proposed and studied for nonlinear Hamiltonian systems. The new algorithm is built upon the SAV approach and the spectral Petrov–Galerkin (SPG) method, which enjoys both the advantages of SAV and SPG methods such as the properties of energy preserving and high order accuracy. A rigorous theoretical analysis is provided to show that the proposed algorithm is well-posed and convergent. Furthermore, the conservation properties are investigated. In particular, we prove that SAV-SPG method preserves the modified energy exactly and maintains the symplectic structure up to a spectral accuracy. Numerical experiments have been conducted to verify the efficacy of our algorithm.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.