Paper Info
Title
Pseudospectral methods based on nonclassical orthogonal polynomials for solving nonlinear variational problems
Abstract
Two direct pseudospectral methods based on nonclassical orthogonal polynomials are proposed for solving finite-horizon and infinite-horizon variational problems. In the proposed finite-horizon and infinite-horizon methods, the rate variables are approximated by the Nth degree weighted interpolant, using nonclassical Gauss-Lobatto and Gauss points, respectively. Exponential Freud type weights are introduced for both of nonclassical orthogonal polynomials and weighted interpolation. It is shown that the absolute error in weighted interpolation is dependent on the selected weight, and the weight function can be tuned to improve the quality of the approximation. In the finite-horizon scheme, the functional is approximated based on Gauss-Lobatto quadrature rule, thereby reducing the problem to a nonlinear programming one. For infinite-horizon problems, an strictly monotonic transformation is used to map the infinite domain onto a finite interval. We transcribe the transformed problem to a nonlinear programming using Gauss quadrature rule. Numerical examples demonstrate the accuracy of the proposed methods.
Year
DOI
Venue
2014
10.1080/00207160.2013.854338
International Journal of Computer Mathematics
Keywords
Field
DocType
nonlinear programming,variational problems,weighted interpolation,infinite-horizon,nonclassical pseudospectral method
Monotonic function,Mathematical optimization,Weight function,Nonlinear system,Orthogonal polynomials,Mathematical analysis,Interpolation,Nonlinear programming,Pseudospectral optimal control,Gaussian quadrature,Mathematics
Journal
Volume
Issue
ISSN
91
7
0020-7160
Citations 
PageRank 
References 
1
0.36
10
Authors
3
Name
Order
Citations
PageRank
Mohammad Maleki1173.53
Ishak Hashim27516.70
Saeid Abbasbandy318026.64