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1.
We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.  相似文献   
2.
保结构算法的相位误差分析及其修正   总被引:2,自引:0,他引:2  
陈璐  王雨顺 《计算数学》2014,36(3):271-290
辛算法和保能量算法是应用最为广泛的两种保结构算法.本文从相位误差的角度给出了他们的比较结果.我们针对线性动力系统,分别分析了基于Pade对角逼近给出的辛算法和基于平均向量场法得到的能量守恒算法的相位误差,并通过数值验证了分析结果.文章还给出了保结构算法相位误差的改进方法,并通过数值例子验证了方法的有效性.  相似文献   
3.
We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Nu- merical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations.  相似文献   
4.
以多辛Euler-box格式为基础对正则长波(RLW)方程的初边值问题进行了讨论,推导了一个新的显式10点格式.模拟孤立波的数值实验表明,这个新的多辛格式是行之有效的,能很好的反映出RLW方程的非弹性性质.  相似文献   
5.
孤立波方程的保结构算法   总被引:4,自引:0,他引:4  
王雨顺  王斌  季仲贞 《计算物理》2004,21(5):386-400
讨论了孤立波方程的保结构差分算法,以一些经典的孤立波方程为例,如KdV,sine-Gordon,K-P方程,给出了它们的辛和多辛结构,说明辛和多辛算法的可适用性.提出局部守恒算法和广义保结构算法的概念,它们是保结构算法的概念自然推广.还给出一种能系统构造局部守恒格式的复合方法.数值例子说明,保结构数值能很好模拟各种孤立波的演化。  相似文献   
6.
In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ||·||2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.  相似文献   
7.
In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local timespace region which is independent of the boundary condition and more essential than the global energy conservation law.Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving(LEP) scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.  相似文献   
8.
We derive a new method for a coupled nonlinear Schr/Sdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.  相似文献   
9.
近来,哈密尔顿偏微分方程多辛算法的研究越来越热门.多辛算法已经成为保结构算法的一个重要分支.对哈密尔顿偏微分方程多辛算法的发展进行了综述,其中包括其基本概念、主要结果和一些应用.此外,文章还部分阐述了多辛算法概念的推广和延伸.  相似文献   
10.
2+1维sine-Gordon方程多辛格式的复合构造   总被引:7,自引:0,他引:7       下载免费PDF全文
以2+1维sine-Gordon方程为例,提出构造多辛算法的一种复合方法, 即: 独立地辛离散多辛偏微分方程的各个方向, 复合这些辛离散格式得到原偏微分方程的多辛算法. 通过这种复合方法, 可以构造任意阶精度的多辛算法,其中包括一些常用算法. 孤立子的数值模拟试验说明所给出的多辛算法是有效的.  相似文献   
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