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A DISSIPATION-PRESERVING INTEGRATOR FOR DAMPED oscillatory HAMILTONIAN systems

Journal of Computational Mathematics 2022年第4期40卷 570-588页

作者： Wei Shi Kai Liu College of Mathematical Sciences Nanjing Tech UniversityNanjing 211816China School of Statistics and Data Science Nanjing Audit UniversityNanjing 210023China

In this paper,based on discrete gradient,a dissipation-preserving integrator for weakly dissipative perturbations of oscillatory Hamiltonian system is *** solution of this system is a damped nonlinear ***,lots of nonlinear oscillatory mechanical systems including frictional forces lend themselves to this *** new integrator gives a discrete analogue of the dissipation property of the original ***,since the integrator is based on the variation-of-constants formula for oscillatory systems,it preserves the oscillatory structure of the *** properties of the new integrator are *** convergence is analyzed for the implicit iterations based on the discrete gradient integrator,and it turns out that the convergence of the implicit iterations based on the new integrator is independent of k Mk,where M governs the main oscillation of the system and usually k Mk≫*** significant property shows that a larger stepsize can be chosen for the new schemes than that for the traditional discrete gradient integrators when applied to the oscillatory Hamiltonian *** experiments are carried out to show the effectiveness and efficiency of the new integrator in comparison with the traditional discrete gradient methods in the scientific literature。

关键词： Weakly dissipative systems oscillatory systems Structure-preserving algorithm Discrete gradient integrator Sine-Gordon equation Continuousα-Fermi-Pasta-Ulam system

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Hexagonal Standing-Wave Patterns in Periodically Forced Reaction-Diffusion systems

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Chinese Physics Letters 2006年第6期23卷 1414-1417页

作者：张可王宏利谯春欧阳颀 School of Physics and State Key Laboratory for Mesoscopic Physics Peking University Beijing 100871

The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.

关键词： oscillatory systems

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Resonance in Defect Turbulence under Periodic External Force

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Chinese Physics Letters 2007年第7期24卷 1849-1852页

作者：谯春冯晓波王宏利欧阳颀 School of Physics and State Key Laboratory for Mesoscopic Physics Peking University Beijing 100871

The periodically forced spatially extended Brusselator is investigated in the chaotic regime. We explore resonant or non-resonant patterns generated under various forcing frequencies and forcing amplitudes. Resonant spatially uniform oscillation and irregular structures are found. Furthermore two types of regular spatial patterns are generated under appropriate parameters. Our results of numerical simulations demonstrate that periodic force can give rise to resonant patterns in forced systems of spatiotemporal chaos similar to the situation of forced systems of regular oscillations.

关键词： oscillatory systems PATTERNS

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Efficient Energy-preserving Methods for General Nonlinear oscillatory Hamiltonian System

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1863-1878页

作者： Yong Lei FANG Chang Ying LIU Bin WANG School of Mathematics and Statistics Zaozhuang University Zaozhuang 277160 P. R. China School of Mathematics and Statistics Nanjing University of Information Science ~ Technology Nanjing 210044 P. R. China School of Mathematical Sciences Qufu Normal University Qufu 273165 P. R. China

In this paper, we propose and analyze two kinds of novel and symmetric energy-preservmg formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq＂（t）＋ Bq（t） = f（q（t））, where A ∈ R^m×m is a symmetric positive definite matrix, B ∈ R^m×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f（q） = -VqV（q） for a real-valued function V（q）. The energy-preserving formulae can exactly preserve the Hamiltonian H（q＇,q） = 1/2q＇^TAq＇＋ 1/2q^TBq - V（q）. We analyze the properties of energy-preserving and convergence of the derived energy-preserving formula and obtain new efficient energy-preserving integrators for practical computation. Numerical experiments are carried out to show the efficiency of the new methods by the nonlinear Hamiltonian systems.

关键词： Nonlinear Hamiltonian wave equations energy-preserving schemes Average Vector Field method oscillatory systems

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