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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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1609-9389
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Volume 14, Issue 1 (Jan 2014)

Issues

High Order Numerical Methods for Fractional Terminal Value Problems

Neville J. Ford
  • Department of Mathematics, University of Chester, CH1 4BJ, UK
  • Email:
/ Maria L. Morgado
  • CM-UTAD, Department of Mathematics, University of Trás-os-Montes e Alto Douro, Quinta de Prados 5001-801, Vila Real, Portugal
  • Email:
/ Magda Rebelo
  • CEMAT-IST/UTL and Department of Mathematics, Faculdade de Ciências e Tecnologia, UNL, Quinta da Torre, 2829-516 Caparica, Portugal
  • Email:
Published Online: 2013-09-21 | DOI: https://doi.org/10.1515/cmam-2013-0022

Abstract.

In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. We provide a convergence analysis of the numerical method, derived based upon properties of the equation being solved and without the need to impose smoothness conditions on the solution. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.

Keywords: Fractional Calculus; Caputo Derivative; Boundary Value Problem; Nonpolynomial Collocation Method; Shooting Method

MSC: 65L05; 34A08; 26Axx

About the article

Published Online: 2013-09-21

Published in Print: 2014-01-01


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2013-0022. Export Citation

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