A nonpolynomial collocation method for fractional terminal value problems

N. J. Ford, Maria Luisa Morgado, M. Rebelo

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper we propose a nonpolynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order alpha, 0 <alpha <1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a nonpolynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples. (C) 2014 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)392-402
Number of pages11
JournalJournal of Computational and Applied Mathematics
Volume275
DOIs
Publication statusPublished - Feb 2015

Keywords

  • Fractional calculus
  • Caputo derivative
  • Boundary value problem
  • Nonpolynomial collocation method
  • VOLTERRA INTEGRAL-EQUATIONS
  • WEAKLY SINGULAR KERNELS
  • PIECEWISE POLYNOMIAL COLLOCATION
  • BOUNDARY-VALUE-PROBLEMS
  • DIFFERENTIAL-EQUATIONS
  • NUMERICAL-SOLUTION

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