A nonpolynomial collocation method for fractional terminal value problems

• Autores: N. J. Ford, M. L. Morgado, Magda Rebelo
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 275, Nº 1, 2015, págs. 392-402
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.06.013
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• Resumen

  • 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 á, 0 < á < 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.