检索结果-内蒙古大学图书馆

Local structure-preserving algorithms for the nonlinear Schrödinger equation with power law nonlinearity

APPLIED MATHEMATICS AND COMPUTATION 2025年 484卷

作者： Luo, Fangwen Tang, Qiong Huang, Yiting Ding, Yanhui Tang, Sijia Hunan Univ Technol Sch Sci Zhuzhou 412007 Hunan Peoples R China

This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schr & ouml;dinger equation with power law nonlinearity, comprising two local energy- conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algorithms to achieve global conservation under periodic boundary conditions. Theoretical analyses confirm the conservation properties of these algorithms. In numerical experiments, we validate the advantages of these algorithms in maintaining longterm energy or momentum conservation by comparing them with a multi-symplectic Preissman algorithm.

关键词： Nonlinear Schr & ouml dinger equation Power law nonlinearity structure-preserving algorithms Local conservation Global conservation

来源：评论

学校读者我要写书评

暂无评论

A Class of Meshless structure-preserving algorithms for the Nonlinear Schrödinger Equation

引用

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 2024年

作者： Wang, Jialing Zhou, Zhengting Lin, Zhoujin Nanjing Univ Informat Sci & Technol Sch Math & Stat Nanjing 210044 Peoples R China

This paper aims to give a unified construction framework of meshless structure-preserving algorithms to solve the d-dimensional ( d = 1 {d=1} or 2) nonlinear Schr & ouml;dinger equation. Based on the method of lines, we first derive a finite-dimensional Hamiltonian system by using the radial basis function method of the quasi-interpolation and the technique of left-multiplying a diagonal matrix to discretize the space direction. Then suitable geometric numerical integrations can be used to discretize the time direction, which yields a class of meshless structure-preserving algorithms. In addition to the construction, the structure-preserving properties and their proofs are also provided in detail. Besides the uniform and nonuniform grids, the numerical experiments on the random grids are also emphasized to verify the theoretical research well, which is of great significance for scattering points based on the characteristics of actual problems.

关键词： The Nonlinear Schr & ouml dinger Equation Meshless Scheme Geometric Numerical Integrations structure-preserving algorithms Random Grids

来源：评论

学校读者我要写书评

暂无评论

Explicit high-order structure-preserving algorithms for the two-dimensional fractional nonlinear Schrodinger equation

引用

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2022年第5期99卷 877-894页

作者： Fu, Yayun Shi, Yanhua Zhao, Yanmin Xuchang Univ Sch Sci Xuchang 461000 Peoples R China

The paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrodinger equation by combing the invariant energy quadratization method and Runge-Kutta method. We first derive the Hamiltonian formulation of the equation, and obtain a new equivalent system via introducing a scalar variable. Then, we propose a semi-discrete conservative system by using the Fourier pseudo-spectral method to approximate the equivalent system in space. Further applying the fourth-order modified Runge-Kutta method to the semi-discrete system gives two classes of schemes for the equation. One scheme preserves the energy while the other scheme conserves the mass. Numerical experiments are provided to demonstrate the conservative properties, convergence orders and long time stability of the proposed schemes.

关键词： Fractional nonlinear Schrodinger equation structure-preserving algorithms invariant energy quadratization Runge-Kutta method explicit conservative schemes

来源：评论

学校读者我要写书评

暂无评论

structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrodinger equation

引用

APPLIED NUMERICAL MATHEMATICS 2020年 156卷 77-93页

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

This paper aims to construct structure-preserving numerical schemes for the two-dimensional space fractional Klein-Gordon-Schrodinger equation, which are based on the newly developed partitioned averaged vector field methods. First, we derive an equivalent equation, and reformulate the equation as an infinite dimensional canonical Hamiltonian system by virtue of the variational derivative of the functional with fractional Laplacian. Then, we use the Fourier pseudo-spectral method to discrete the equation in space direction and obtain a semi-discrete conservative system, which can be reformulated a finite dimensional canonical Hamiltonian system. Further applying the partitioned averaged vector field methods to the semi-discrete system gives a class of fully-discrete schemes that can preserve the mass and energy exactly. Numerical examples are provided to confirm our theoretical analysis results at last. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： structure-preserving algorithms Fractional Klein-Gordon-Schrodinger equation Hamiltonian system Partitioned averaged vector field methods

来源：评论

学校读者我要写书评

暂无评论

LOCAL structure-preserving algorithms FOR THE KDV EQUATION

引用

Journal of Computational Mathematics 2017年第3期35卷 289-318页

作者： Jialing Wang Yushun Wang Jiangsu Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing 210023 China

In this paper, based on the concatenating method, we present a unified framework to construct a series of local structure-preserving algorithms for the Korteweg-de Vries （KdV） equation, including eight multi-symplectic algorithms, eight local energy-conserving algo- rithms and eight local momentum-conserving algorithms. Among these algorithms, some have been discussed and widely used while the most are new. The outstanding advantage of these proposed algorithms is that they conserve the local structures in any time-space re- gion exactly. Therefore, the local structure-preserving algorithms overcome the restriction of global structure-preserving algorithms on the boundary conditions. Numerical experiments are conducted to show the performance of the proposed methods. Moreover, the unified framework can be easily applied to many other equations.

关键词： Korteweg-de Vries （KdV） equation structure-preserving algorithms Concate-nating method Multi-symplectic conservation law.

来源：评论

学校读者我要写书评

暂无评论

Three sixth-order explicit symplectic Runge-Kutta-Nystrom methods with exact parameters

引用

RESULTS IN APPLIED MATHEMATICS 2025年 26卷

作者： Pan, Mengjiao Zhang, Jingjing Zhang, Shangyou East China Jiaotong Univ Sch Sci Nanchang 330013 Peoples R China Univ Delaware Dept Math Sci Newark DE 19716 USA

For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge-Kutta-Nystr & ouml;m methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge-Kutta method and two approximate 6-th order symplectic explicit Runge-Kutta-Nystr & ouml;m methods. These new methods are more accurate and stable.

关键词： Symplectic schemes structure-preserving algorithms Explicit runge-kutta-nystr & ouml m method Geometric numerical integration

来源：评论

学校读者我要写书评

暂无评论

An exact in time Fourier pseudospectral method with multiple conservation laws for three-dimensional Maxwell's equations

引用

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS 2024年第3期58卷 857-880页

作者： Wang, Bin Jiang, Yaolin Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shannxi Peoples R China

Maxwell's equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell's equations. This is accomplished by combining Fourier pseudospectral methods in space and exact formulation in time. Fast computation is efficiently implemented in the scheme by using the matrix diagonalisation method and fast Fourier transform algorithm which are well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and exact in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests.

关键词： Maxwell's equations exact in time Fourier pseudospectral method Duhamel's formula structure-preserving algorithms convergence

来源：评论

学校读者我要写书评

暂无评论

Efficiency energy-preserving cosine pseudo-spectral algorithms for the sine-Gordon equation with Neumann boundary conditions

引用

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2022年第12期99卷 2367-2381页

作者： Yue, Xiaopeng Fu, Yayun Xuchang Univ Sch Sci Henan Joint Int Res Lab High Performance Computat Xuchang 461000 Peoples R China

This paper considers the newly introduced generalized scalar auxiliary variable approaches to construct high-efficiency energy-preserving schemes for the sine-Gordon equation with Neumann boundary conditions. The equation is first reformulated into an equivalent system by defining a new auxiliary variable that is not limited to square root. Then, the cosine pseudo-spectral method is applied to the system and derive a semi-discrete conservative scheme. Subsequently, we combine the auxiliary variable with the nonlinear term and use an explicit technique discretization in time to derive a fully-discrete energy-preserving scheme. Furthermore, a fast algorithm based on the discrete cosine transform technique reduces the computational complexity in practical computation. Finally, various numerical experiments are displayed to verify the accuracy, efficiency and conservation of the proposed schemes.

关键词： structure-preserving algorithms generalized scalar auxiliary sine-Gordon equation cosine pseudo-spectral method Neumann boundary

来源：评论

学校读者我要写书评

暂无评论

A Class of Explicit Divergence-Free Methods for Maxwell's Equations With Dirichlet Boundary Conditions

引用

IEEE ACCESS 2022年 10卷 126188-126198页

作者： Zeng, Xianyang Yang, Hongli Nanjing Inst Technol Ind Ctr Nanjing Peoples R China Nanjing Inst Technol Sch Math & Phys Nanjing Peoples R China

In this paper, we focus on the numerical solutions of Maxwell's equations with Dirichlet boundary conditions in rectangular coordinate. A class of explicit methods is derived by using an effective solver for a system of ordinary differential equations which is obtained by approximating on spatial fields. A significant advantage of this class of methods is their simplicity and their ease of implementation. The error estimates presented in this paper show that the numerical solutions obtained by this class of methods is of high-order. The main advantage of this class of methods is that it is divergence-free.

关键词： Maxwell equations Boundary conditions Time-domain analysis Mathematical models Electromagnetic propagation Ordinary differential equations Numerical models Computation theory Dirichlet boundary value problem divergence-free methods electromagnetic propagation Maxwell's equations time-domain methods structure-preserving algorithms

来源：评论

学校读者我要写书评

暂无评论

Exponential discrete gradient schemes for a class of stochastic differential equations

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年 402卷 113797-113797页

作者： Ruan, Jialin Wang, Lijin Wang, Pengjun Univ Chinese Acad Sci Sch Math Sci YuQuan Rd 19 Beijing 100049 Peoples R China

In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving properties of the schemes for SDEs with special structures are investigated. Numerical tests are performed to verify the theoretical results and illustrate the numerical behavior of the proposed methods. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Stochastic differential equations Exponential integrators Discrete gradient methods Mean-square convergence structure-preserving algorithms

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：