SPECTRAL_METHOD

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EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION
《Journal of Computational Mathematics》2024年第4期1032-1062,共31页Suna Ma Huiyuan Li Zhimin Zhang Hu Chen Lizhen Chen 
supported by the National Natural Science Foundation of China(Grant No.12101325)and by the NUPTSF(Grant No.NY220162);The second author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,11971016);The third author was supported by the National Natural Science Foundation of China(Grant No.12131005);The fifth author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,U2230402).
An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained ex...
关键词：Integral fractional Laplacian Spectral method Eigenvalue problem Regularity analysis Error estimate 
A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION
《Journal of Computational Mathematics》2021年第1期22-42,共21页Haiyan Jiang Tiao Lu Xu Yin 
This research was supported in part by the NSFC(91434201,91630130,11671038,11421101).
This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value problem...
关键词：Finite diference method Spectral method Hybrid scheme Error analysis Wigner equation. 
HIGH ORDER FINITE DIFFERENCE/SPECTRAL METHODS TO A WATER WAVE MODEL WITH NONLOCAL VISCOSITY
《Journal of Computational Mathematics》2020年第4期580-605,共26页Mohammad Tanzil Hasan Chuanju Xu 
The research of this author is partially supported by NSF of China(51661135011 and 91630204).
In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave.By using the Caputo fractional derivative definition...
关键词：Water waves Nonlocal viscosity Finite difference Spectral method Conver-gence order Decay rate 
NUMERICAL APPROXIMATION OF THE SMOLUCHOWSKI EQUATION USING RADIAL BASIS FUNCTIONS
《Journal of Computational Mathematics》2020年第1期176-194,共19页Christiane Helzel Maximilian Schneiders 
The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis funct...
关键词：Smoluchowski equation Spectral method Radial basis function method 
A MULTI-DOMAIN SPECTRAL IPDG METHOD FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBER
《Journal of Computational Mathematics》2013年第2期107-136,共30页Lunji Song Jing Zhang Li-Lian Wang 
The work of the first author was partially supported by the National Natural Science Foundation of China （11026065 and 11101196）. This work was largely done when this author worked as a Research Fellow in Nanyang Technological University. The work of the second author was supported by the National Natural Science Foundation of China （11201166）. The work of the third author was supported by Singapore MOE Tier 1 Grant （2013-2016）, and Singapore A＊STAR-SERC-PSF Grant 122-PSF-0007.
This paper is concerned with a multi-domain spectral method, based on an interior penalty discontinuous Galerkin （IPDG） formulation, for the exterior Helmholtz problem truncated via an exact circular or spherical Di...
关键词：Helmholtz equation High wavenumber Global DtN boundary condition IPDG Multli-domain spectral method. 
SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS被引量：1
《Journal of Computational Mathematics》2012年第6期579-600,共22页Tianjun Wang Benyu Guo Wei Li 
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are es...
关键词：Three-dimensional Legendre approximation in Jacobi weighted Sobolev space Lifting technique Spectral method for mixed inhomogeneous boundary value problems. 
SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS被引量：1
《Journal of Computational Mathematics》2010年第3期418-428,共11页Lin Wang Ziqing Xie Zhimin Zhang 
supported in part by the Programme for New Century Excellent Talents in University (NCET-06-0712);the National Natural Science Foundation of China (NSFC 10871066, 10571053);Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University;supported in part by the US National Science Foundation grant DMS-0612908
We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise con...
关键词：EIGENVALUE Spectral method COLLOCATION Galerkin finite element method. 
A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS被引量：13
《Journal of Computational Mathematics》2009年第2期254-265,共12页Ishtiaq Ali Hermann Brunner 
The research of HB was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Research Grants Council of Hong Kong;The research of TT was supported by Hong Kong Baptist University,the Research Grants Council of Hong Kong and he was supported in part by the Chinese Academy of Sciences while visiting its Institute of Computational Mathematics.
We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approx...
关键词：Spectral methods Legendre quadrature formula Pantograph-type delay differential equations Error analysis Exponential convergence 
ON SPECTRAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS AND THE CONVERGENCE ANALYSIS被引量：34
《Journal of Computational Mathematics》2008年第6期825-837,共13页Tao Tang Xiang XU Jin Cheng 
supported by CERG Grants of Hong Kong Research Grant Council;FRG grants of Hong Kong Baptist University
The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equatio...
关键词：Legendre-spectral method Second kind Volterra integral equations Convergence analysis. 
CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM被引量：2
《Journal of Computational Mathematics》2006年第4期451-462,共12页Sang Dong Kim Byeong Chun Shin 
We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares func...
关键词：Least-squares methods Spectral method Negative norm. 
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