An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
Joint Authors
Hashim, Ishak
Maleki, Mohammad
Abbasbandy, Saeid
Kajani, Majid Tavassoli
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-17
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Maleki, Mohammad& Hashim, Ishak& Kajani, Majid Tavassoli& Abbasbandy, Saeid. 2012. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-467598
Modern Language Association (MLA)
Maleki, Mohammad…[et al.]. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems. Abstract and Applied Analysis No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-467598
American Medical Association (AMA)
Maleki, Mohammad& Hashim, Ishak& Kajani, Majid Tavassoli& Abbasbandy, Saeid. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-467598
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-467598