SPECTRAL

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ANALYSIS OF TWO ANY ORDER SPECTRAL VOLUME METHODS FOR 1-D LINEAR HYPERBOLIC EQUATIONS WITH DEGENERATE VARIABLE COEFFICIENTS
《Journal of Computational Mathematics》2024年第6期1627-1655,共29页Minqiang Xu Yanting Yuan Waixiang Cao Qingsong Zou 
supported by the NSFC(Grants 92370113,12071496,12271482);Moreover,the first author was also supported by the Zhejiang Provincial NSF(Grant LZ23A010006);by the Key Research Project of Zhejiang Lab(Grant 2022PE0AC01);the fourth author was also supported by the Guangdong Provincial NSF(Grant 2023A1515012097).
In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th o...
关键词：Spectral Volume Methods L^(2)stability Error estimates SUPERCONVERGENCE 
SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES
《Journal of Computational Mathematics》2024年第1期111-133,共23页Ruihan Guo Yan Xu 
supported by NSFC(Grant No.11601490).Research of Y.Xu is supported by NSFC(Grant No.12071455).
In[20],a semi-implicit spectral deferred correction(SDC)method was proposed,which is efficient for highly nonlinear partial differential equations(PDEs).The semi-implicit SDC method in[20]is based on first-order time ...
关键词：Spectral deferred correction method Nonlinear PDEs Local discontinuous Galerkin method Second-order scheme 
GRAPH SPARSIFICATION BY UNIVERSAL GREEDY ALGORITHMS
《Journal of Computational Mathematics》2023年第4期741-770,共30页Ming-Jun Lai Jiaxin Xie Zhiqiang Xu 
supported by NSFC grant(Nos.12001026,12071019);supported by the National Science Fund for Distinguished Young Scholars grant(No.12025108);Beijing Natural Science Foundation(No.Z180002);NSFC grant(Nos.12021001,11688101).
Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications,such as simplification of social networks,least squares problems,and numerical solution of symmetric posit...
关键词：Spectral sparsification Subset selection Greedy algorithms Graph clustering Linear sketching 
CONVERGENCE OF LAPLACIAN SPECTR A FROM R ANDOM SA MPLES
《Journal of Computational Mathematics》2020年第6期952-984,共33页Wenqi Tao Zuoqiang Shi 
This research was supported by NSFC Grant 11671005.
Eigenvectors and eigenvalues of discrete Laplacians are often used for manifold learning and nonlinear dimensionality reduction.Graph Laplacian is one widely used discrete laplacian on point cloud.It was previously pr...
关键词：Graph Laplacian Laplacian spectra Random samples Spectral convergence 
STABILIZED BARZILAI-BORWEIN METHOD被引量：2
《Journal of Computational Mathematics》2019年第6期916-936,共21页Oleg Burdakov Yuhong Dai Na Huang 
Part of this work was done during Oleg Burdakovs visit to the Chinese Academy of Sciences;which was supported by the Visiting Scientist award under the Chinese Academy of Sciences President's International Fellowship Initiative for 2017;The second author was supported by the Chinese Natural Science Foundation(No.11631013);the National 973 Program of China(No.2015CB856002).
The Barzilai-Borwein(BB)method is a popular and efficient tool for solving large-scale unconstrained optimization problems.Its search direction is the same as for the steepest descent(Cauchy)method,but its stepsize ru...
关键词：UNCONSTRAINED optimization SPECTRAL ALGORITHMS STABILIZATION CONVERGENCE analysis. 
WEAK ERROR ESTIMATES FOR TRAJECTORIES OF SPDEs UNDER SPECTRAL GALERKIN DISCRETIZATION
《Journal of Computational Mathematics》2018年第2期159-182,共24页Charles-Edouard Brehier Martin Hairer Andrew M. Stuart 
We consider stochastic semi-linear evolution equations which are driven by additive, spatially correlated, Wiener noise, and in particular consider problems of heat equation （analytic semigroup） and damped-driven wa...
关键词：Stochastic Partial Differential Equations Weak approximation Spectral Galerkin discretization 
HIGH ORDER LOCAL DISCONTINUOUS GALERKIN METHODS FOR THE ALLEN-CAHN EQUATION： ANALYSIS AND SIMULATION被引量：3
《Journal of Computational Mathematics》2016年第2期135-158,共24页Ruihan Guo Liangyue Ji Yan Xu 
In this paper, we present a local discontinuous Galerkin （LDG） method for the AllenCahn equation. We prove the energy stability, analyze the optimal convergence rate of k ＋ 1 in L2 norm and present the （2k＋1）-th...
关键词：Local discontinuous Galerkin method Allen-Cahn equation Energy stability Convex splitting Spectral deferred correction A priori error estimate Negative norm errorestimate. 
SPECTRAL AND SPECTRAL ELEMENT METHODS FOR HIGH ORDER PROBLEMS WITH MIXED BOUNDARY CONDITIONS被引量：1
《Journal of Computational Mathematics》2014年第4期392-411,共20页Benyu Guo Chao Zhang 
In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and pro...
关键词：Spectral and spectral element methods~ High order problems with mixedinhomogeneous boundary conditions. 
A NOTE ON JACOBI SPECTRAL-COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS被引量：10
《Journal of Computational Mathematics》2013年第1期47-56,共10页Yanping Chen Xianjuan Li Tao Tang 
Acknowledgments. This work is supported by National Science Foundation of China （1127114 5）, Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme （2008）, Specialized Research Fund for the Doctoral Program of Higher Education （20114407110009）, and the Project of Department of Education of Guangdong Province （No. [2012] 290）. The second author is sup- ported by the Natural Science Foundation of Fujian Province, China （2012J01007） and Start-up fund of Fuzhou University （0460022456）. The second and third author are supported by the FRG Grant of Hong Kong Baptist University and the RGC Grants provided by Research Grant Council of Hong Kong.
This work is concerned with spectrM Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form （t - s）-a When the underlying solutions are sufficiently smooth, t...
关键词：Volterra integral equations Convergence analysis Spectral-collocation meth-ods. 
SUPERGEOMETRIC CONVERGENCE OF SPECTRAL COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS被引量：4
《Journal of Computational Mathematics》2011年第6期698-719,共22页Can Huang Tao Tang Zhimin Zhang 
This research is partially supported by the GRF grants of Hong Kong Research Grant Council; the FRG grants of Hong Kong Baptist University; the US National Science Foundation through grant DMS-0612908; the Ministry of Education of China through the Changjiang Scholars program; and Guangdong Provincial Government of China through the ＂Computational Science Innovative Research Team＂ program.
A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of fun...
关键词：Weakly singular kernel Integro-differential equations Collocation method. 
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