共查询到18条相似文献,搜索用时 480 毫秒
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高斯光束在光伏光折变晶体中孤立波的演化满足傍轴方程.傍轴方程可以看作无限维Hamil-tonian系统并可以利用辛几何算法进行计算.数值结果表明外加电场和光伏场的强弱和入射高斯光束的振辐对形成稳定的孤立波有显著的影响.傍轴方程的辛几何差分格式能很好地模拟傍轴方程中孤立波的演化行为. 相似文献
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近年来,学者们对发展型偏微分方程设计了一种能保持多个守恒律的数值方法,这类方法无论在解的精度还是长时间的数值模拟方面都表现出非常好的性质.将这类思想应用到三阶Airy方程,即三阶散射方程,对其设计了满足两个守恒律的非线性差分格式.该格式不仅计算数值解,同时计算数值能量,并且保证数值解和数值能量同时守恒.从数值结果可以看出,该格式在长时间的数值模拟中具有更好的保结构性质. 相似文献
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有限振幅T-S波在非平行边界层中的非线性演化研究 总被引:2,自引:0,他引:2
研究对非平行边界层稳定性有重要影响的非线性演化问题,导出与其相应的抛物化稳定性方程组,发展了求解有限振幅T-S波的非线性演化的高效数值方法。这一数值方法包括预估-校正迭代求解各模态非线性方程并避免模态间的耦合,采用高阶紧致差分格式,满足正规化条件,确定不同模态非线性项表和数值稳定地作空间推进。通过给出T-S波不同的初始幅值,研究其非线性演化。算例与全Navier-Stokes方程的直接数值模拟(DNS)的结果作了比较。 相似文献
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In this paper, a new high-order energy-preserving scheme is proposed for the modified Korteweg-de Vries equation. The proposed scheme is constructed by using the Hamiltonian boundary value methods in time, and Fourier pseudospectral method in space. Exploiting this method, we get second-order and fourth-order energy-preserving integrators. The proposed schemes not only have high accuracy, but also exactly conserve the total mass and energy in the discrete level. Finally, single solitary wave and the interaction of two solitary waves are presented to illustrate the effectiveness of the proposed schemes. 相似文献
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The fourth order average vector field (AVF) method is applied to solve
the "Good" Boussinesq equation. The semi-discrete system of the "good" Boussinesq
equation obtained by the pseudo-spectral method in spatial variable, which is a
classical finite dimensional Hamiltonian system, is discretized by the fourth order
average vector field method. Thus, a new high order energy conservation scheme of
the "good" Boussinesq equation is obtained. Numerical experiments confirm that the
new high order scheme can preserve the discrete energy of the "good" Boussinesq
equation exactly and simulate evolution of different solitary waves well. 相似文献
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In this paper, a new linearized energy-preserving Crank-Nicolson finite volume element scheme is derived for the improved Boussinesq equation. The fully discrete scheme can be shown to conserve both mass and energy in the discrete setting. It is proved that the scheme is uniquely solvable and convergent with the rate of order two in a discrete L2 norm. At last, a series of numerical experiments on typical improved Boussinesq and Sine–Gordon equations are provided to verify our theoretical results and to show the efficiency and accuracy of the proposed scheme. 相似文献
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The mathematical modeling of a planar solid‐liquid interface in the solidification of a dilute binary alloy is formulating by one of nonintegrable, nonlinear evolution equation known as Sivashinsky equation. In the first part of this paper, the mathematical modeling of Sivashinsky equation is briefly discussed. Since, the exact solutions of this equation is yet unknown, obtaining its numerical solution plays an important role to simulate its behavior. Therefore, in the second part, a second‐order splitting finite difference scheme, based on Crank‐Nicolson method, is investigated to approximate the solution of the Sivashinsky equation with homogeneous boundary conditions. We prove the solvability of the present scheme and establish the error estimate of the numerical scheme. 相似文献
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Evolution of solitary waves in photovoltaic-photorefractive crystal satisfy the paraxial equation. The paraxial equation is transformed into the symplectic structure of the infinite dimensional Hamiltonian system. The symplectic structure of the paraxial equation is discretizated by the symplectic method. The corresponding symplectic scheme preserves conservation of discrete energy which reflects conservation of energy of the paraxial equation. The symplectic scheme is applied to simulate the solitary wave behaviors of the paraxial equation. Evolution of the solitary waves with the different applied electric field and the different photovoltaic fields are investigated. 相似文献
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The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the two-dimensional space-fractional nonlinear Schrödinger equation. First, we reformulate the equation as an canonical Hamiltonian system, and obtain a new equivalent system via introducing a scalar variable. Then, we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction. After that, applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version. As expected, the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step. Finally, numerical experiments are provided to demonstrate the efficiency and conservation of the scheme. 相似文献