A numerical solution of problems in calculus of variation using direct method and nonclassical parameterization

Authors:
Mohammad Maleki;Mahmoud Mashali-Firouzi
Affiliations:
Department of Mathematics, Payame Noor University (PNU), Isfahan, Iran;Department of Mathematics, School of Mohajer, Hezar Jerib Street, Isfahan, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
Cited 0

Control parametrization: a unified approach to optimal control problems with general constraints

Automatica (Journal of IFAC)
Direct and indirect methods for trajectory optimization

Annals of Operations Research - Special issue on nonlinear methods in economic dynamics and optimal control: Gmo¨or-series No. 2
Legendre wavelets direct method for variational problems

Mathematics and Computers in Simulation
A spectral solution of the Sturm-Liouville equation: comparison of classical and nonclassical basis sets

Journal of Computational and Applied Mathematics
The use of He's variational iteration method for solving variational problems

International Journal of Computer Mathematics
Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem

International Journal of Computer Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper a direct method for solving variational problems using nonclassical parameterization is presented. A nonclassical parameterization based on nonclassical orthogonal polynomials is first introduced to reduce a variational problem to a nonlinear mathematical programming problem. Then, using the Lagrange multiplier technique the problem is converted to that of solving a system of algebraic equations. Illustrative examples are given to demonstrate the validity and applicability of the technique.