Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method

Mohammad Maleki, Ishak Hashim, Saeid Abbasbandy, A. Alsaedi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper presents an adaptive Legendre-Gauss pseudospectral method for solving a type of constrained fractional variational problems (FVPs). The fractional derivative is defined in the Caputo sense. In the presented method, by dividing the domain of the problem into a uniform mesh the given FVP reduces to a nonlinear mathematical programming problem, and there is no need to solve the complicated fractional Euler-Lagrange equations. The method developed in this paper adjusts both the mesh spacing and the number of collocation points on each subinterval in order to improve the accuracy. The method is easy to implement and yields very accurate results. Some error estimates and convergence properties of the method are discussed. Numerical examples are included to confirm the efficiency and convergence of the proposed method.

Original languageEnglish
Pages (from-to)41-57
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume283
DOIs
Publication statusPublished - 1 Aug 2015

Fingerprint

Pseudospectral Method
Adaptive Method
Nonlinear programming
Variational Problem
Fractional
Derivatives
Mesh
Euler-Lagrange Equations
Fractional Derivative
Legendre
Collocation
Mathematical Programming
Nonlinear Programming
Convergence Properties
Gauss
Spacing
Error Estimates
Numerical Examples

Keywords

  • Adaptive pseudospectral method
  • Caputo derivative
  • Fractional variational problem
  • Nonlinear programming
  • Shifted Legendre-Gauss points

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method. / Maleki, Mohammad; Hashim, Ishak; Abbasbandy, Saeid; Alsaedi, A.

In: Journal of Computational and Applied Mathematics, Vol. 283, 01.08.2015, p. 41-57.

Research output: Contribution to journalArticle

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