A Legendre rational spectral method is proposed for the nonlinear Klein-Gordon equation on the whole line. Its stability and convergence are proved. Numerical results coincides well with the theoretical analysis and d...A Legendre rational spectral method is proposed for the nonlinear Klein-Gordon equation on the whole line. Its stability and convergence are proved. Numerical results coincides well with the theoretical analysis and demonstrate the e?ciency of this approach.展开更多
An orthogonal system of rational functions is derived from the mapped Laguerre polynomials,which is used for numerical solution of singular differential equations.A model problem is considered.A multiple-step algorith...An orthogonal system of rational functions is derived from the mapped Laguerre polynomials,which is used for numerical solution of singular differential equations.A model problem is considered.A multiple-step algorithm is developed to implement this method.Numerical results show the efficiency of this new approach.展开更多
A,novel collocation method for a coupled system of singularly perturbed linear equations is presented.This method is based on rational spectral collocation method in barycentric form with sinh transform.By sinh transf...A,novel collocation method for a coupled system of singularly perturbed linear equations is presented.This method is based on rational spectral collocation method in barycentric form with sinh transform.By sinh transform,the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution.The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform.Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.展开更多
基岩面埋深是公路工程建设中的重要参考依据。本文通过福建地区两个探测实例,研究了微动H/V谱比法探测基岩面埋深的方法技术,介绍了微动H/V(Horizontal to Vertical)谱比法提取基岩面埋深的方法原理。首先对微动单个三分量检波器采集地...基岩面埋深是公路工程建设中的重要参考依据。本文通过福建地区两个探测实例,研究了微动H/V谱比法探测基岩面埋深的方法技术,介绍了微动H/V(Horizontal to Vertical)谱比法提取基岩面埋深的方法原理。首先对微动单个三分量检波器采集地震记录进行处理和分析,获取了测点的峰值频率F 0。在钻孔较多的情况下,可根据钻孔的中风化岩深度与峰值频率F 0的幂函数拟合,得到了该区的经验参数a和b,从而可以计算整个测区每个测点的中风化岩深度三维分布。在钻孔较少的情况下,可根据测区内部分钻孔的孔内剪切波值计算该区的覆盖层平均横波速度,进而根据经验公式计算覆盖层厚度和基岩面三维埋深分布。两个探测实例研究结果表明:微动H/V谱比法是一种快速获取公路工程三维基岩面的方法,在一定条件下,相对误差能够控制在5%左右,能够满足工程勘察的需求。微动谱比法具有简便性和易操作性,点位可随机布置,几乎不受场地条件限制,能够取得较好的地质效果,可推广应用。展开更多
The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numeri...The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.展开更多
基金This work is supported in part by NSF of China, N.10471095, SF of Shanghai N.04JC14062, The Fund of ChineseEducation Ministry N.20040270002, The Shanghai Leading Academic Discipline Project N. T0401, The Funds forE-institutes of Universities N.E03004 and The special Funds for Major Specialities and N.04DB15 of ShanghaiEducation Commission.
文摘A Legendre rational spectral method is proposed for the nonlinear Klein-Gordon equation on the whole line. Its stability and convergence are proved. Numerical results coincides well with the theoretical analysis and demonstrate the e?ciency of this approach.
基金The work of this author is supported by The Foundation of CAEP 20030658)The work of this author is partially supported by The Shanghai Natural Science Foundation N.00JC14057+1 种基金The Shanghai Natural Science Foundation for Youth N. 01QN85.The work of thi
文摘An orthogonal system of rational functions is derived from the mapped Laguerre polynomials,which is used for numerical solution of singular differential equations.A model problem is considered.A multiple-step algorithm is developed to implement this method.Numerical results show the efficiency of this new approach.
基金support from the National Natural Science Foundation of China under Grants No.10671146 and No.50678122 is acknowledged.The authors are grateful to the referee and the editor for helpful comments and suggestions.
文摘A,novel collocation method for a coupled system of singularly perturbed linear equations is presented.This method is based on rational spectral collocation method in barycentric form with sinh transform.By sinh transform,the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution.The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform.Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
文摘基岩面埋深是公路工程建设中的重要参考依据。本文通过福建地区两个探测实例,研究了微动H/V谱比法探测基岩面埋深的方法技术,介绍了微动H/V(Horizontal to Vertical)谱比法提取基岩面埋深的方法原理。首先对微动单个三分量检波器采集地震记录进行处理和分析,获取了测点的峰值频率F 0。在钻孔较多的情况下,可根据钻孔的中风化岩深度与峰值频率F 0的幂函数拟合,得到了该区的经验参数a和b,从而可以计算整个测区每个测点的中风化岩深度三维分布。在钻孔较少的情况下,可根据测区内部分钻孔的孔内剪切波值计算该区的覆盖层平均横波速度,进而根据经验公式计算覆盖层厚度和基岩面三维埋深分布。两个探测实例研究结果表明:微动H/V谱比法是一种快速获取公路工程三维基岩面的方法,在一定条件下,相对误差能够控制在5%左右,能够满足工程勘察的需求。微动谱比法具有简便性和易操作性,点位可随机布置,几乎不受场地条件限制,能够取得较好的地质效果,可推广应用。
文摘The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.
