BDF-type shifted Chebyshev approximation scheme for fractional functional differential equations with delay and its error analysis

2017 ◽  
Vol 118 ◽  
pp. 266-276 ◽  
Author(s):  
V.G. Pimenov ◽  
A.S. Hendy
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Approximation Scheme ◽  
Functional Differential Equations ◽  
Chebyshev Approximation ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Equations With Delay ◽  
Fractional Functional

scholarly journals Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. G. Pimenov ◽  
A. S. Hendy
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
True Solution ◽  
New Approach ◽  
Numerical Studies ◽  
Runge Kutta Method ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Equations With Delay ◽  
Fractional Functional

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.

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