SPECTRAL_METHOD

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A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems
《Advances in Applied Mathematics and Mechanics》2023年第3期568-582,共15页Juan Zhang Jiabin Song Huanzhen Chen 
This work was partly supported by National Natural Science Foundation of China(Grant Nos.:12101283,12271233 and 12171287);Natural Science Foundation of Shandong Province(Grant Nos.:ZR2019YQ05,2019KJI003,and ZR2016JL004).
The fractional optimal control problem leads to significantly increased computational complexity compared to the corresponding classical integer-order optimal control problem,due to the global properties of fractional...
关键词：Fractional optimal control problem state constraint spectral method Jacobi polynomial a priori error estimate 
Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions
《Advances in Applied Mathematics and Mechanics》2022年第6期1302-1332,共31页Shengnan Kang Kenzu Abdella Macro Pollanen Shuhua Zhang Liang Wang 
the Natural Sciences and Engineering Research Council of Canada,and the National Natural Science Foundation of China(Nos.11771322,and 72071140).
This paper presents the numerical solution of the time-dependent Gross-Pitaevskii Equation describing the movement of quantum mechanics particles under non-homogeneous boundary conditions.Due to their inherent non-lin...
关键词：Quantum mechanics spectral method time-dependent partial differential equation boundary value problem. 
Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations
《Advances in Applied Mathematics and Mechanics》2018年第6期1440-1458,共19页Xingfa Yang Yin Yang Yanping Chen Jie Liu 
The author would like to thank the referees for the helpful suggestions.The work was supported by NSFC Project(Nos.11671342,91430213,11671157 and 11771369);Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2018JJ2374);Key Project of Hunan Provincial Department of Education(No.17A210).
In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo sense.Using the properties of the Caputo derivative,we convert the fractional ...
关键词：Spectral method NONLINEAR fractional derivative Volterra integro-differential equations Caputo derivative 
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 
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