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 
A Semi-Lagrangian Spectral Method for the Vlasov-Poisson System Based on Fourier, Legendre and Hermite Polynomials
《Communications on Applied Mathematics and Computation》2019年第3期333-360,共28页Lorella Fatone Daniele Funaro Gianmarco Manzini 
In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the appro...
关键词：Spectral METHODS SEMI-LAGRANGIAN METHODS HIGH-ORDER HERMITE functions Vlasov-Poisson equations Mass conservation 
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 
Parameters Identification of Continuous-Time Hammerstein System with Advanced Gauss Pseudo spectral Method
《Journal of Donghua University(English Edition)》2016年第5期803-808,共6页何颖 戴明祥 杨新民 易文俊 
Assembly Fund,China(No.9140C3007081005)
An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approx...
关键词：minimization Legendre controllable converge canonical verify transcribed interpolation derivative affine 
Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations被引量：1
《Advances in Applied Mathematics and Mechanics》2015年第1期74-88,共15页Yin Yang Yanping Chen Yunqing Huang Wei Yang 
supported by National Science Foundation of China(11301446,11271145);Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009);the Project of Department of Education of Guangdong Province(2012KJCX0036);China Postdoctoral Science FoundationGrant(2013M531789);Project of Scientific Research Fund ofHunan Provincial Science and Technology Department(2013RS4057);the Research Foundation of Hunan Provincial Education Department(13B116).
A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in ...
关键词：Spectral method NONLINEAR Volterra integral equations 
A Stochastic Collocation Method for Delay Differential Equations with Random Input
《Advances in Applied Mathematics and Mechanics》2014年第4期403-418,共16页Tao Zhou 
the National Natural Science Foundation of China(No.91130003 and No.11201461).
In this work,we concern with the numerical approach for delay differential equations with random coefficients.We first show that the exact solution of the problem considered admits good regularity in the random space,...
关键词：Delay differential equations stochastic collocation sparse grid legendre spectral method 
A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay被引量：1
《Advances in Applied Mathematics and Mechanics》2013年第2期131-145,共15页Weishan Zheng Yanping Chen 
This work is supported by National Science Foundation of China(11271145);Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009);the Project of Department of Education of Guangdong Province(2012KJCX0036).
In this paper,a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph delay.We provide a rigorous error analysis for the proposed method.The spec...
关键词：Legendre-spectral method second order Volterra integro-differential equation pantograph delay error analysis 
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. 
A LEGENDRE GALERKIN SPECTRAL METHOD FOR OPTIMAL CONTROL PROBLEMS被引量：1
《Journal of Systems Science & Complexity》2011年第4期663-671,共9页Yanping CHEN Nianshi XIA Nianyu YI 
supported by the Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008);the National Natural Science Foundation of China under Grant No.10971074
This paper considers the Legendre Galerkin spectral approximation for the unconstralnea optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control...
关键词：Legendre-Galerkin optimal control spectral 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 
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