A Legendre Galerkin spectral method for optimal control problems |
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| Authors: | Yanping Chen Nianshi Xia Nianyu Yi |
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| Institution: | 1.School of Mathematical Sciences,South China Normal University,Guangzhou,China;2.The Faculty of Mathematics, Chengyi College,Jimei University,Xiamen,China;3.Hunan Key Laboratory for Computation and Simulation in Science and Engineering; School of Mathematics and Computational Science,Xiangtan University,Xiangtan,China |
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| Abstract: | This paper considers the Legendre Galerkin spectral approximation for the unconstrained optimal control problems. The authors
derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate
basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform
to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented. |
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