SPECTRAL_METHOD

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A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels
《Numerical Mathematics(Theory,Methods and Applications)》2022年第4期1041-1062,共22页Chao Zhang Guoqing Yao Sheng Chen 
The research of C.Zhang is partially supported by NSFC(Grant Nos.11971207,12071172);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.20KJA11002);The research of S.Chen is partially supported by NSFC(Grant No.11801235).
In this paper,we propose a hybrid spectral method for a type of nonlocal problems,nonlinear Volterra integral equations(VIEs)of the second kind.The main idea is to use the shifted generalized Log orthogonal functions(...
关键词：Nonlocal problem Volterra integral spectral element method log orthogonal function Legendre polynomial weak singularity exponential convergence 
Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem被引量：2
《Numerical Mathematics(Theory,Methods and Applications)》2013年第3期499-519,共21页Xingyang Ye Chuanju Xu 
The work of X.Y was partially supported by the Natural Science Foundation of Fujian Province,China(Grant No.2012J01013);The work of C.X.was partially supported by National NSF of China(Grants 11071203 and 91130002).
An inverse problem of reconstructing the initial condition for a time fractional diffusion equation is investigated.On the basis of the optimal control framework,the uniqueness and first order necessary optimality co...
关键词：Time fractional diffusion equation inverse problem spectral method error estimate conjugate gradient method. 
Laguerre Spectral Method for High Order Problems
《Numerical Mathematics(Theory,Methods and Applications)》2013年第3期520-537,共18页Chao Zhang Ben-Yu Guo Tao Sun 
The work of the first author is supported in part by NSF of China No.11171227;Research Fund for young teachers of Jiangsu Normal University No.11XLR27;and Priority Academic Program Development of Jiangsu Higher Education Institutions.The work of the second author is supported in part by NSF of China No.11171227;Fund for Doctoral Authority of China No.20123127110001;Fund for Einstitute of Shanghai Universities No.E03004;and Leading Academic Discipline Project of Shanghai Municipal Education Commission No.J50101.
In this paper,we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions.It is also available for approximated solutions growing fast at infinity.The spectral accura...
关键词：Laguerre spectral method high order problems with mixed inhomogeneous boundary conditions 
A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel被引量：1
《Numerical Mathematics(Theory,Methods and Applications)》2013年第2期424-446,共23页Yunxia Wei Yanping Chen 
supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008);National Science Foundation of China(10971074);Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009).
This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation with a weakly singular kernel.The solution of this equati...
关键词：Neutral Volterra integro-differential equation weakly singular kernel Jacobi collocation discretization convergence analysis 
The Dissipative Spectral Methods for the First Order Linear Hyperbolic Equations被引量：1
《Numerical Mathematics(Theory,Methods and Applications)》2012年第3期493-508,共16页Lian Chen Zhongqiang Zhang Heping Ma 
supported by National Natural Science Foundation of China(11171209);Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50101);Specialized Research Fund for the Doctoral Program of Higher Education(20060280010);Graduate Innovative Foundation of Shanghai University(SHUCX091048).
In this paper,we introduce the dissipative spectral methods(DSM)for the first order linear hyperbolic equations in one dimension.Specifically,we consider the Fourier DSM for periodic problems and the Legendre DSM for ...
关键词：First order hyperbolic equation dissipative spectral method error estimate 
A Triangular Spectral Method for the Stokes Equations被引量：2
《Numerical Mathematics(Theory,Methods and Applications)》2011年第2期158-179,共22页Lizhen Chen Jie Shen Chuanju Xu 
supported by NFS grant DMS-0915066;supported by the National Natural Scheme Foundation of China(Grant number 11071203).
A triangular spectral method for the Stokes equations is developed in this paper.The main contributions are two-fold:First of all,a spectral method using the rational approximation is constructed and analyzed for the ...
关键词：Stokes equations triangular spectral method error analysis 
Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type
《Numerical Mathematics(Theory,Methods and Applications)》2011年第1期38-52,共15页Yanzhao Cao Li Yin 
This work is supported by the National Natural Science Foundation of China(10701014,10871029);a grant from the Laboratory of Computational Physics,and the Foundation of China Academy of Engineering Physics;The authors thank the anonymous referees for helpful comments which improve the presentation of the paper.
This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in multi-dimensions.Convergence analysis and error estimates are presented for the n...
关键词：Stochastic differential equation spectral method error estimates white noise 
An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains
《Numerical Mathematics(Theory,Methods and Applications)》2009年第3期258-274,共17页Qirong Fang Jie Shen Li-Lian Wang 
supported in part by NSF grant DMS-0610646;supported by AcRF Tier 1 Grant RG58/08;Singapore MOE Grant T207B2202;Singapore NRF2007IDM-IDM002-010
An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper.The method is based on the so called transformed field expansio...
关键词：Acoustic scattering high-order methods boundary perturbations spectral-Galerkinmethods. 
Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions被引量：3
《Numerical Mathematics(Theory,Methods and Applications)》2009年第1期43-64,共22页Xiao-Yong Zhang Ben-Yu Guo Yu-Jian Jiao 
supported in part by NSF of China N.10871131;The Science and Technology Commission of Shanghai Municipality,Grant N.075105118;Shanghai Leading Academic Discipline Project N.T0401;Fund for E-institute of Shanghai Universities N.E03004.
In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve ...
关键词：Generalized Laguerre-spherical harmonic spectral method Cauchy problem of nonlinear Klein-Gordon equation. 
Legendre Rational Spectral Method for Nonlinear Klein-Gordon Equation被引量：3
《Numerical Mathematics A Journal of Chinese Universities(English Series)》2006年第2期143-149,共7页Zhongqing Wang Benyu Guo 
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.
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...
关键词：勒让德有理数光谱方法 非线性方程 克莱因-戈登方程 收敛 稳定性 
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