Pell-Lucas Collocation Method for Solving High-Order Functional Differential Equations with Hybrid Delays
Pell-Lucas Collocation Method for Solving High-Order Functional Differential Equations with Hybrid Delays
In this study, thePell-Lucas collocation method has been presented to solve high-order linearfunctional differential equations with hybrid delays under mixed conditions.The proposed method is based on the matrix forms of Pell-Lucas polynomials andtheir derivatives, along with the collocation points. The used techniquereduces the problem to a matrix equation corresponding to a set of algebraicequations with the unknown Pell-Lucas coefficients. In addition, an erroranalysis based on residual function is performed and some numerical examplesare presented to show the efficiency and accuracy of the method.
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- Reutskiy, S. Yu. A new collocation method for approximate
solution of the pantograph functional differential equations with
proportional delay, Applied Mathematics and Computation, 2015,
266, 642-655.
-
El-Khatib, M. A. Convergenue of the spline function for
functional differential equation of neutral type, International
J0urnal of Computer Mathematics. 2003, 80(11), 1437-1447.
- Rashed, M. T. Numerical solution of functional differential,
integral and integro- differential equations, Applied Mathematics
and Computation, 2004, 156, 485-492.
- Bhrawy, A. H, Assas, L. M, Tohidi, E, Alghamdi, M. A. A
Legendre-Gauss collocation method for neutral functional
differential equations with proportional delays, Advances in
Difference Equations, 2013, (2013), 63.
- Heydari, M. Loghmani, G. B. Hosseini, S. M. Operational
matrices of Chebyshev cardinal functions and their aplication for
solving delay differential equations arising in electrodynamics
with error estimation, Applied Mathematical.Modeling, 2013, 37,
7789-7809.
- Sedaghat, S. Ordokhani, Y. Dehghan, M. Numerical solution of
the delay differential equations of pantograph type via Chebyshev
polynomials, Common Nonlinear Science Numerical Simulation,
2012, 17, 4815-4830.
- Akyüz, A. Sezer, A Chebyshev Collocation method for the
solution of linear integro- differential equations, International
Journal of Computer Mathematics, 1999, 72 (4) 491-507.
- Gürbüz, B. Gülsu, M. Sezer, M. Numerical approach of high-
order linear delay-difference equations with variable coefficients
in terms of Laguerre polynomials, Mathematical and
Computational Applications, 2011, 16, 267-278.
- Wang, W. S. Li, S. F. On the one-leg Q-methods for solving
nonlinear neutral functional differential equations, Applied
Mathematics and Computation, 2007, 193 (1),285-301.
- Cheng, X. Chen, Z. Zhang, Q. An approximate solution for a
neutral functional- differential equation with proportional delays,
Applied Mathematics and Computation, 2015, 260 27-34.
- Kürkçü, Ö.K. Aslan, E. Sezer, M. A Novel Collocation Method
Based on Residual Error Analysis for Solving Integro-Differential
Equations Using Hybrid Dickson and Taylor Polynomials, Sains
Malaysiana, 2017, 46, 2335–347.
- Dai, C. Zhang, J. Jacobian elliptic function method for nonlinear
differential difference equations, Chaos, Solitons & Fractals,
2006, 27, 1042-1047.
- Çelik, İ. Collocation method and residual correction using
Chebyshev series, Applied Mathematics and Computation,
2006, 174, 910–920.
- Wei, Y. Chen, Y. Legendre spectral collocation method for
neutral and high-order Volterra integro-differential equation,
Applied Numeric Mathematics, 2014, 81, 15–29.
- Wang, K. Wang, Q. Lagrange collocation method for solving
Volterra–Fredholm integral equations, Applied Mathematics
and Computation, 2013, 219 10434–10440.
- Sezer, M. Daşçıoğlu, A. Taylor polynomial solutions of
general linear differantial-difference equations with variable
coefficients. Applied Mathematics and Computation, 2006, 174,
1526-1538.
- Sezer, M., Taylor polynomial solution of Volterra integral
equations, International Journal of Mathematical Education in
Science and Technology, 1994, 25, 625–633.
- Sezer, M. and Kaynak, M. Chebyshev polynomial solutions of
linear differential equations, International Journal of
Mathematical Education in Science and Technology, 1996, 27,
607–618.
- A.F.Horadam and J.M. Mahon, Pell and Pell-Lucas
Polynomials, Fibonacci Quartery, 23(1), 17-20, (1985).
- P. Filipponi, A. F. Horadam, Second derivative sequences of
Fibonacci and Lucas polynomials, Fibonacci Quarterly, 31(3)
(1993), 194-204.