A Chebyshev spectral method for time-varying two-point boundary-value and optimal control problems

A numerical method for solving two-point boundary-value problems with time-varying coefficients is presented in this paper. The method is based on constructing the Nth degree polynomial interpolation using Chebyshev's nodes to approximate the solution of linear two-point value problems with tim...

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Bibliographic Details
Published in:International journal of computer mathematics 2005-02, Vol.82 (2), p.193-202
Main Authors: Elnagar, Gamal, Zafiris, Vasilis
Format: Article
Language:English
Subjects:
Cell averaging
Chebyshev spectral method
Optimal control
Two-point boundary-value problem
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Summary:A numerical method for solving two-point boundary-value problems with time-varying coefficients is presented in this paper. The method is based on constructing the Nth degree polynomial interpolation using Chebyshev's nodes to approximate the solution of linear two-point value problems with time-varying coefficients. The method can be applied to obtain the optimal control of linear time-varying systems subject to quadratic cost criteria. The two-point value problem and the optimal control problem are thereby transformed into a programming problem. The method is simple and efficient, and yields very accurate results. Illustrative examples are included to demonstrate the accuracy of method.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160412331296652