An adaptive pseudospectral method for fractional order boundary value problems

Mohammad Maleki, Ishak Hashim, Majid Tavassoli Kajani, Saeid Abbasbandy

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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 to 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 Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

Original languageEnglish
Article number381708
JournalAbstract and Applied Analysis
Volume2012
DOIs
Publication statusPublished - 2012

Fingerprint

Pseudospectral Method
Integrodifferential equations
Adaptive Method
Fractional Order
Boundary value problems
Volterra Integro-differential Equations
Boundary Value Problem
Polynomials
Derivatives
Fractional
Integration by parts
Unknown
Interpolation
Polynomial Interpolation
Singular Integrals
Fractional Derivative
Legendre
Collocation
Algebraic Equation
Gauss

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

An adaptive pseudospectral method for fractional order boundary value problems. / Maleki, Mohammad; Hashim, Ishak; Kajani, Majid Tavassoli; Abbasbandy, Saeid.

In: Abstract and Applied Analysis, Vol. 2012, 381708, 2012.

Research output: Contribution to journalArticle

Maleki, Mohammad ; Hashim, Ishak ; Kajani, Majid Tavassoli ; Abbasbandy, Saeid. / An adaptive pseudospectral method for fractional order boundary value problems. In: Abstract and Applied Analysis. 2012 ; Vol. 2012.
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