共查询到18条相似文献,搜索用时 93 毫秒
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DGH方程作为一类重要的非线性水波方程有着许多广泛的应用前景.基于Hamilton系统的多辛理论研究了一类强色散DGH方程的数值解法,利用多辛普雷斯曼方法构造了一种典型的半隐式的多辛格式.分析了该格式的局部能量和动量守恒律误差,并给出了数值算例.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性. 相似文献
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《数学物理学报(A辑)》2016,(6)
DGH方程作为一类重要的非线性方程有着许多广泛的应用前景.通过正则变化,构造了DGH方程的多辛哈密尔顿系统.利用Fourier拟谱方法对此哈密尔顿系统进行数值离散,并构造了一种半隐式的多辛格式.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性. 相似文献
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广义Boussinesq方程的多辛方法 总被引:1,自引:1,他引:0
广义Boussinesq方程作为一类重要的非线性方程有着许多有趣的性质,基于Hamilton空间体系的多辛理论研究了广义Boussinesq方程的数值解法,构造了一种等价于多辛Box格式的新隐式多辛格式,该格式满足多辛守恒律、局部能量守恒律和局部动量守恒律.对广义Boussinesq方程孤子解的数值模拟结果表明,该多辛离散格式具有较好的长时间数值稳定性. 相似文献
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利用F展开法与指数函数法相结合的方法,在相关文献的基础上,重新研究了Zhiber-Shabat方程,获得了许多与现有文献中解的表达式不相同的各种精确解.这些解同样具有孤立波解,纽子波解和周期波解的各种动力学特征.从而丰富了相关文献中关于Zhiber-Shabat波方程的孤立子解和周期解的种类. 相似文献
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Zhiber-Shabat方程的孤立波解与周期波解 总被引:1,自引:1,他引:0
结合齐次平衡法原理并利用F展开法,再次研究了Zhiber-Shabat方程的各种椭圆函数周期解.当椭圆函数的模m分别趋于1或0时,利用这些椭圆函数周期解,得到了Zhiber-Shabat方程的各种孤子解和三角函数周期解,从而丰富了相关文献中关于Zhiber-Shabat波方程的解的类型. 相似文献
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带乘性噪声的空间分数阶随机非线性Schrödinger方程是一类重要的方程,可应用于描述开放非局部量子系统的演化过程.该方程为一个无穷维分数阶随机Hamilton系统,且具有广义多辛结构和质量守恒的性质.针对该方程的广义多辛形式,在空间上采用拟谱方法离散分数阶微分算子,在时间上则采用隐式中点格式,构造出一类保持全局质量的广义多辛格式.对行波解和平面波解等进行数值模拟,结果验证了所构造格式的有效性和保结构性质,时间均方收敛阶约在0.5到1之间. 相似文献
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In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method. 相似文献
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In this paper, we find that the Ito-type coupled KdV equation can be written as a multi-symplectic Hamiltonian partial differential equation (PDE). Then, multi-symplectic Fourier pseudospectral method and multi-symlpectic wavelet collocation method are constructed for this equation. In the numerical experiments, we show the effectiveness of the proposed methods. Some comparisons between the proposed methods are also made with respect to global conservation properties. 相似文献
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Junjie Wang 《计算数学(英文版)》2015,33(4):379-395
The higher order wave equation of KdV type, which describes many important physical
phenomena, has been investigated widely in last several decades. In this work, multi-symplectic formulations for the higher order wave equation of KdV type are presented,
and the local conservation laws are shown to correspond to certain well-known Hamiltonian
functionals. The multi-symplectic discretization of each formulation is calculated by the
multi-symplectic Fourier pseudospectral scheme. Numerical experiments are carried out,
which verify the efficiency of the Fourier pseudospectral method. 相似文献
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《Journal of Computational and Applied Mathematics》2012,236(6):1354-1369
In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov–Kuznetsov (ZK) equation and the Kadomtsev–Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method. 相似文献
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Yaming Chen Songhe SongHuajun Zhu 《Journal of Computational and Applied Mathematics》2011,236(6):1354-1369
In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method. 相似文献
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In this article, an exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed for solving the nonlinear Schrödinger equation with wave operator. The numerical method is based on a Deuflhard-type exponential wave integrator for temporal integration and the Fourier pseudospectral method for spatial discretizations. The scheme is fully explicit and very efficient thanks to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established by means of the mathematical induction. Numerical results are reported to confirm the theoretical studies. 相似文献
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Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier-type pseudospectral methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave phenomena. 相似文献
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Handan Borluk Gulcin M. Muslu 《Numerical Methods for Partial Differential Equations》2015,31(4):995-1008
In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi‐discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995–1008, 2015 相似文献