SPECTRAL_METHOD

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Modified Legendre Rational Spectral Method for Burgers Equation on the Whole Line
《Journal of Mathematical Study》2022年第4期415-431,共17页Liutao Tian Yujian Jiao 
supported in part by the National Natural Science Foundation of China(Grant Nos.12271365,11771299 and 12171141);Nature Science Fundation of Shanghai(Grant Nos.22ZR1445400 and 20JC1413800).
In this paper,we propose a spectral method for the Burgers equation using the modified Legendre rational functions,and prove its generalized stability and convergence.Numerical results demonstrate the efficiency of th...
关键词：Burgers equation spectral method modified Legendre rational functions problem on the whole line 
Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils
《Journal of Mathematical Study》2020年第1期12-44,共33页Fatima Aboud Francois Jauberteau Guy Moebs Didier Robert 
supported by the research project DefiMaths of the Federation de Mathematiques des Pays de la Loire,CNRS FR 2962;supported by the CIMPA(International Center of Pure ans Applied Mathematics);Computations are done thanks to the computer of the CCIPL(Centre de Calcul Intensif des Pays de la Loire).
In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators.This leads to solve nonlinear eigenvalue problems.We begin with a review of theoretical results for the...
关键词：Nonlinear eigenvalue problems SPECTRA PSEUDOSPECTRA finite difference methods Galerkin spectral method Hermite functions. 
Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations
《Journal of Mathematical Study》2018年第3期253-293,共41页Hongyi Zhu Laurence Cherfils Alain Miranville Shuiran Peng Wen Zhang 
The work of Z.W.was supported by the National Natural Science Foundation of China(Grant 11861007,11761007);Research Foundation of Educa-tion Bureau of Jiangxi Province(Grant GJJ160564);Doctoral Scientific Research Foundation(Grant DHBK2017148)
Our aim in this paper is to study a fully discrete scheme for modified higher-order(in space)anisotropic generalized Cahn-Hilliard models which have extensive applications in biology,image processing,etc.In particular...
关键词：Modified Cahn-Hilliard equation higher-order models energy stability ANISOTROPY 
Generalized Hermite Spectral Method for Nonlinear Fokker-Planck Equations on the Whole Line
《Journal of Mathematical Study》2018年第2期177-195,共19页Guo Chai Tian-jun Wang 
The first author of this work was supported in part by NSF of China No.11401380;The second author was supported in part by NSF of China No.11371123,No.11571151 and No.11771299
In this paper,we develop a spectral method for the nonlinear Fokker-Planck equations modeling the relaxation of fermion and boson gases.A full-discrete general-ized Hermite spectral scheme is constructed.Its convergen...
关键词：Nonlinear Fokker-Planck equations the whole line generalized Hermite spectral method full-discrete scheme 
A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line被引量：3
《Journal of Mathematical Study》2018年第2期196-213,共18页Xuhong Yu Yunge Zhao Zhongqing Wang 
This work was supported in part by NSF of China No.11571238 and No.11601332;the Hujiang Foundation of China No.B14005
A diagonalized Legendre rational spectral method for solving second and fourth order differential equations are proposed.Some Fourier-like Sobolev orthogo-nal basis functions are constructed which lead to the diagonal...
关键词：Legendre rational spectral method Sobolev orthogonal functions elliptic boundary value problems heat equation numerical results 
Numerical Assessment of a Class of High Order Stokes Spectrum Solver
《Journal of Mathematical Study》2018年第1期1-14,共14页Etienne Ahusborde Mejdi Azaiez Ralf Gruber 
It iswell known that the approximation of eigenvalues and associated eigenfunctions of a linear operator under constraint is a difficult problem.One of the difficulties is to propose methods of approximation which sat...
关键词：Stokes eigenvalues problem spectral method 
A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations被引量：1
《Journal of Mathematical Study》2018年第1期57-75,共19页Hua Wu Yunzhen Zhu Hailu Wang Lingfang Xu 
supported by the National Natural Science Foundation of China(grant number 11571225).
We develop a domain decomposition Chebyshev spectral collocationmethod for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions.The method is easy to implement and possesses hi...
关键词：Nonlinear Volterra integral equations domain decomposition method Chebyshev–collocation spectral method convergence analysis 
Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction被引量：1
《Journal of Mathematical Study》2014年第1期1-20,共20页Jing An Jie Shen 
This work is Supported in part by NSF of China grants 91130002 and 11371298。
An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem.We develop in this paper efficient and accurate spectral meth...
关键词：spectral method index of refraction transmission eigenvalue electromagnetic scattering inverse problem 
Spectral Method for the Black-Scholes Model of American Options Valuation被引量：2
《Journal of Mathematical Study》2014年第1期47-64,共18页Haiming Song Ran Zhang WenYi Tian 
This work was supported by the National Natural Science Foundation of China(Grant Nos.11271157,11371171);the Open Project Programof the State Key Lab of CAD&CG(A1302)of Zhejiang University and the Scientific Research Foundation for Returned Scholars,Ministry of Education of China.
In this paper,we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model.The optimal exercise boundary which satisfies a nonlinear Volterra integral equ...
关键词：American option pricing Black-Scholes model optimal exercise boundary frontfixing Chebyshev spectral method Runge-Kutta method 
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