An adaptive pseudospectral method for fractional order boundary value problems
type: Item
instance of: scholarly article
title: An adaptive pseudospectral method for fractional order boundary value problems
zbMATH Open document ID: 1261.34009
DOI: 10.1155/2012/381708
author: Mohammad Maleki
author: Majid Tavassoli Kajani
author: I. Hashim
author: Saeid Abbasbandy
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP) which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE). By dividing the interval of the problem into subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG) collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples, including the Bagley-Torvik equation, the proposed method is shown to be efficient and accurate.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6134073
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/381708
OpenAlex ID: W2036943210
Wikidata QID: Q58696471
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description: scientific article; zbMATH DE number 6134073