检索结果-内蒙古大学图书馆

Efficient schemes for the coupled Schrodinger-KdV equations: Decoupled and conserving three invariants

APPLIED MATHEMATICS LETTERS 2018年 86卷 200-207页

作者： Cai, Jiaxiang Bai, Chuanzhi Zhang, Haihui Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China

We give a systematic method for discretizing Hamiltonian partial differential equations. An application of the method to the Hamiltonian form of the coupled Schrodinger-KdV equations yields a temporal first-order conservative scheme. Temporal second- and fourth-order schemes are developed by employing the composition method. All the schemes are decoupled and exactly conserve three invariants simultaneously. Numerical results show good performance of the schemes and verify the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Schrodinger-KdV equation Decoupled scheme Hamiltonian system Discrete gradient method structure-preserving algorithm

来源：评论

学校读者我要写书评

暂无评论

Efficient local structure-preserving schemes for the RLW-type equation

引用

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2017年第5期33卷 1678-1691页

作者： Cai, Jiaxiang Hong, Qi Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China China Acad Engn Phys Grad Sch Beijing 100088 Peoples R China

The multisymplectic schemes have been used in numerical simulations for the RLW-type equation successfully. They well preserve the local geometric property, but not other local conservation laws. In this article, we propose three novel efficient local structure-preserving schemes for the RLW-type equation, which preserve the local energy exactly on any time-space region and can produce richer information of the original problem. The schemes will be mass- and energy-preserving as the equation is imposed on appropriate boundary conditions. Numerical experiments are presented to verify the efficiency and invariant-preserving property of the schemes. Comparisons with the existing nonconservative schemes are made to show the behavior of the energy affects the behavior of the solution.(c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1678-1691, 2017

关键词： conservation law regularized long-wave equation structure-preserving algorithm

来源：评论

学校读者我要写书评

暂无评论

ON A NONLINEAR MATRIX EQUATION ARISING IN NANO RESEARCH

引用

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2012年第1期33卷 235-262页

作者： Guo, Chun-Hua Kuo, Yueh-Cheng Lin, Wen-Wei Univ Regina Dept Math & Stat Regina SK S4S 0A2 Canada Natl Univ Kaohsiung Dept Appl Math Kaohsiung 811 Taiwan Natl Taiwan Univ Dept Math Taipei 106 Taiwan Natl Chiao Tung Univ Ctr Math Modelling & Sci Comp Hsinchu 300 Taiwan

The matrix equation X + A (vertical bar) X(-1)A - Q arises in Green's function calculations in nano research, where A is a real square matrix and Q is a real symmetric matrix dependent on a parameter and is usually indefinite. In practice one is mainly interested in those values of the parameter for which the matrix equation has no stabilizing solutions. The solution of interest in this case is a special weakly stabilizing complex symmetric solution X-*, which is the limit of the unique stabilizing solution X-eta of the perturbed equation X + A(inverted perpendicular) X(-1)A = Q + i eta I, as eta -> 0(+). It has been shown that a doubling algorithm can be used to compute X-eta efficiently even for very small values of eta, thus providing good approximations to X-*. It has been observed by nano scientists that a modified fixed-point method can sometimes be quite useful, particularly for computing X-eta for many different values of the parameter. We provide a rigorous analysis of this modified fixed-point method and its variant and of their generalizations. We also show that the imaginary part X-I of the matrix X-* is positive semidefinite and we determine the rank of X-I in terms of the number of unimodular eigenvalues of the quadratic pencil lambda(2)A(inverted perpendicular) - lambda Q + A. Finally we present a new structure-preserving algorithm that is applied directly on the equation X + A(inverted perpendicular) X(-1)A = Q. In doing so, we work with real arithmetic most of the time.

关键词： nonlinear matrix equation complex symmetric solution weakly stabilizing solution fixed-point iteration structure-preserving algorithm Green's function

来源：评论

学校读者我要写书评

暂无评论

Efficient high-order structure-preserving methods for the generalized Rosenau-type equation with power law nonlinearity

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2018年 59卷 122-131页

作者： Cai, Jiaxiang Liang, Hua Zhang, Chun Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China

Based on the multi-symplectic Hamiltonian formula of the generalized Rosenau-type equation, a multi-symplectic scheme and an energy-preserving scheme are proposed. To improve the accuracy of the solution, we apply the composition technique to the obtained schemes to develop high-order schemes which are also multi-symplectic and energy-preserving respectively. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results verify that all the proposed schemes have satisfactory performance in providing accurate solution and preserving the discrete mass and energy invariants. Numerical results also show that although each basic time step is divided into several composition steps, the computational efficiency of the composition schemes is much higher than that of the non-composite schemes. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Rosenau-type equation Composition method Spectral method Multi-symplectic conservation law structure-preserving algorithm

来源：评论

学校读者我要写书评

暂无评论

Local energy- and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis

引用

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2017年第4期33卷 1329-1351页

作者： Cai, Jiaxiang Hong, Jialin Wang, Yushun Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210046 Jiangsu Peoples R China Chinese Acad Sci State Key Lab Sci & Engn Comp Inst Computat Math & Sci Engn Comp AMSS Beijing 100190 Peoples R China

In this article, we obtain local energy and momentum conservation laws for the Klein-Gordon-Schrodinger equations, which are independent of the boundary condition and more essential than the global conservation laws. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose local energy- and momentum-preserving schemes for the equations. The merit of the proposed schemes is that the local energy/momentum conservation law is conserved exactly in any time-space region. With suitable boundary conditions, the schemes will be charge- and energy-/momentum-preserving. Nonlinear analysis shows LEP schemes are unconditionally stable and the numerical solutions converge to the exact solutions with order O(2+h2). The theoretical properties are verified by numerical experiments. (c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1329-1351, 2017

关键词： conservation law convergence analysis Klein-Gordon-Schrodinger equations local structure structure-preserving algorithm

来源：评论

学校读者我要写书评

暂无评论

An efficient energy-preserving method for the two-dimensional fractional Schrodinger equation

引用

APPLIED NUMERICAL MATHEMATICS 2021年 165卷 232-247页

作者： Fu, Yayun Xu, Zhuangzhi Cai, Wenjun Wang, Yushun Xuchang Univ Sch Sci Xuchang 461000 Peoples R China Nanjing Normal Univ Jiangsu Collaborat Innovat Ctr Biomedial Funct Ma Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210023 Peoples R China

In this paper, we study the Hamiltonian structure and develop a novel energy-preserving scheme for the two-dimensional fractional nonlinear Schrodinger equation. First, we present the variational derivative of the functional with fractional Laplacian to derive the Hamiltonian formula of the equation and obtain an equivalent system by defining a scalar variable. An energy-preserving scheme is then presented by applying exponential time differencing approximations for time integration and Fourier pseudo-spectral discretization in space. The proposed scheme is a linear system and can be solved efficiently. Numerical experiments are displayed to verify the conservation, efficiency, and good performance at a relatively large time step in long time computations. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Fractional nonlinear Schrodinger equation Hamiltonian structure structure-preserving algorithm Exponential time differencing

来源：评论

学校读者我要写书评

暂无评论

Quadratic conservative scheme for relativistic Vlasov-Maxwell system

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2019年 379卷 32-50页

作者： Shiroto, Takashi Ohnishi, Naofumi Sentoku, Yasuhiko Tohoku Univ Dept Aerosp Engn Aoba Ku 6-6-01 Aramaki Aza Aoba Sendai Miyagi 9808579 Japan Osaka Univ Inst Laser Engn 2-6 Yamadaoka Suita Osaka 5650871 Japan

For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solved the first-principle equations of kinetic plasmas, such as the relativistic Vlasov-Maxwell system. This fatal problem is brought by the fact that both the Vlasov and Maxwell equations are indirectly associated with the conservation laws by means of some mathematical manipulations. Here we propose a quadratic conservative scheme, which can strictly maintain the conservation laws by discretizing the relativistic Vlasov-Maxwell system. A discrete product rule and summation-by-parts are the key players in the construction of the quadratic conservative scheme. Numerical experiments of the relativistic two-stream instability and relativistic Weibel instability prove the validity of our computational theory, and the proposed strategy will open the doors to the first-principle studies of mesoscopic and macroscopic plasma physics. (C) 2018 The Author(s). Published by Elsevier Inc.

关键词： Computational plasma physics Relativistic Vlasov-Maxwell system structure-preserving algorithm Quadratic conservative scheme

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of nonlinear matrix equations arising from Green's function calculations in nano research

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2012年第17期236卷 4166-4180页

作者： Guo, Chun-Hua Kuo, Yueh-Cheng Lin, Wen-Wei Univ Regina Dept Math & Stat Regina SK S4S 0A2 Canada Natl Univ Kaohsiung Dept Appl Math Kaohsiung 811 Taiwan Natl Chiao Tung Univ Dept Appl Math Hsinchu 300 Taiwan

The Green's function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form X + (C* + i eta D*)X-1(C + i eta D) = R+i eta P. where R and P are Hermitian, P + lambda D* + lambda D-1 is positive definite for all lambda on the unit circle, and eta -> 0(+). For each fixed eta > 0, we show that the required solution is the unique stabilizing solution X-eta. Then X-center dot = lim(eta -> 0+) X-eta is a particular weakly stabilizing solution of the matrix equation X + C*X-1C = R. In nano applications, the matrices R and C are dependent on a parameter, which is the system energy E. In practice one is mainly interested in those values of g for which the equation X + C*X-1C = R has no stabilizing solutions or, equivalently, the quadratic matrix polynomial P(lambda) = lambda C-2* - lambda R + C has eigenvalues on the unit circle. We point out that a doubling algorithm can be used to compute X-eta efficiently even for very small values eta, thus providing good approximations to X-*. We also explain how the solution X-* can be computed directly using subspace methods such as the QZ algorithm by determining which unimodular eigenvalues of P(lambda) should be included in the computation. In some applications the matrices C, D, R, P have very special sparsity structures. We show how these special structures can be exploited to drastically reduce the complexity of the doubling algorithm for computing X-eta. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Nonlinear matrix equation Weakly stabilizing solution structure-preserving algorithm Green's function

来源：评论

学校读者我要写书评

暂无评论

Decoupled conservative schemes for computing dynamics of the strongly coupled nonlinear Schrodinger system

引用

APPLIED NUMERICAL MATHEMATICS 2020年 157卷 276-290页

作者： He, Zhu Cai, Jiaxiang Shen, Bangyu Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China

Two types of first-order decoupled conservative schemes are firstly proposed for the strongly coupled nonlinear Schrodinger system by using pseudospectral method in space and coordinate increment discrete gradient method in time. And then, in order to improve the solution accuracy in time, the composition methods are employed to construct secondand fourth-order schemes. The proposed schemes are efficient for the system in d >= 2 dimensions and also easy to code because of their decoupled feature. A fast solver is proposed to speed up the computation. Ample numerical examples including the motion of single soliton and interaction of multiple solitary waves are carried out to exhibit the performance of the schemes. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Schrodinger equation structure-preserving algorithm Hamiltonian system Discrete gradient method Energy-preserving algorithm

来源：评论

学校读者我要写书评

暂无评论

Local energy-preserving algorithms for nonlinear fourth-order Schrodinger equation with trapped term

引用

APPLIED MATHEMATICS AND COMPUTATION 2017年 296卷 23-32页

作者： Cai, Jiaxiang Liang, Hua Yang, Bin Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China

Based on the rule that numerical algorithms should preserve the intrinsic properties of the original problem as many as possible, we propose two local energy-preserving algorithms for the nonlinear fourth-order Schrodinger equation with a trapped term. The local energy conservation law is preserved on any local time-space region. With appropriate boundary conditions, the first algorithm will be both globally charge- and energy-preserving and the second one will be energy-preserving. Numerical experiments show that the proposed algorithms provide more accurate solution than many existing methods and also exhibit excellent performance in preserving conservation laws. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Schrodinger equation structure-preserving algorithm Local property Conservation law Energy

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：