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Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations
Joint Authors
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-29
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics.
FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations.
In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs.
This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials.
It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given.
Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method.
Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach.
American Psychological Association (APA)
Pimenov, V. G.& Hendy, A. S.. 2015. Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1052063
Modern Language Association (MLA)
Pimenov, V. G.& Hendy, A. S.. Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations. Abstract and Applied Analysis No. 2015 (2015), pp.1-12.
https://search.emarefa.net/detail/BIM-1052063
American Medical Association (AMA)
Pimenov, V. G.& Hendy, A. S.. Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1052063
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052063