FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS

SEZER, Mehmet; KURT, Ayşe; YALÇINBAŞ, Salih

FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS

Ayşe KURT, (Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey)

Salih YALÇINBAŞ, (Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey)

Mehmet SEZER (Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey)

Mathematical and Computational Applications

6 0

Yıl: 2013 Cilt: 18 Sayı: 3 Sayfa Aralığı: 448 - 458 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS

Öz:

This study presents a new method for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions. We introduce a Fibonacci collocation method based on the Fibonacci polynomials for the approximate solution. Numerical examples are included to demonstrate the applicability of the technique. The obtained results are compared by the known results.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

1. R. P. Kanwal and K. C. Liu, A Taylor expansion approach for solving integral equations, International Journal of Mathematical Education 20,411-414, 1989.
2. M. K. Kadalbajoo and K. K. Sharma, Numerical analysis of singularly perturbed delay differential equations with layer behaviour, Applied Mathematics and Computation 157, 11-28, 2004.
3. H. Zuoshang, Boundness of solutions to functional integro- differential equations, Proceedings of the American Mathematical Society 114 (2), 1992.
4. C. E. Elmer and E. S. Van Vleck, Analysis and Computation of Traveling Wave Solutions of Bistable Differential-Difference Equations, Nonlinearity 12 (4), 771-798, 1999.
5. M. Gülsu and M. Sezer, A Taylor polynomial approach for solving differentialdifference equations, Journal of Computational and Applied Mathematics 186, 217-225, 2006.
6. M. Sezer and A. Akyüz-Daşcıoğlu, Taylor polynomial solutions of general linear differential-difference equations, Applied Mathematics and Computation 174, 1526- 1538, 2006.
7. K. Erdem, S. Yalçınbaş, Bernoulli Polynomial Approach to High-Order Linear Differential-Difference Equations, AIP Conference Proceedings 1479, 360-364, 2012.
8. M. Sezer, A method for the approximate solution of the second order linear differential equations in terms of Taylor polynomials, International Journal of Science and Mathematics Education 27 (6), 821-834, 1996.
9. S. Yalçınbaş, N. Özsoy and M. Sezer, Approximate solution of higher order linear differential equations by means of a new rational Chebyshev collocation method, Mathematical and Computational Applications 15(1), 45-56, 2010.
10. S. Yalçınbaş and M. Sezer, The approximate solution of high-order linear Volterra- Fredholm integro differential equations in terms of Taylor polynomials. Applied Mathematics and Computation 112, 291-308, 2000.
11. S. Yalçınbaş, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Applied Mathematics and Computation 127, 195-206, 2002.

APA	KURT A, YALÇINBAŞ S, SEZER M (2013). FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. , 448 - 458.
Chicago	KURT Ayşe,YALÇINBAŞ Salih,SEZER Mehmet FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. (2013): 448 - 458.
MLA	KURT Ayşe,YALÇINBAŞ Salih,SEZER Mehmet FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. , 2013, ss.448 - 458.
AMA	KURT A,YALÇINBAŞ S,SEZER M FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. . 2013; 448 - 458.
Vancouver	KURT A,YALÇINBAŞ S,SEZER M FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. . 2013; 448 - 458.
IEEE	KURT A,YALÇINBAŞ S,SEZER M "FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS." , ss.448 - 458, 2013.
ISNAD	KURT, Ayşe vd. "FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS". (2013), 448-458.

APA	KURT A, YALÇINBAŞ S, SEZER M (2013). FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. Mathematical and Computational Applications, 18(3), 448 - 458.
Chicago	KURT Ayşe,YALÇINBAŞ Salih,SEZER Mehmet FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. Mathematical and Computational Applications 18, no.3 (2013): 448 - 458.
MLA	KURT Ayşe,YALÇINBAŞ Salih,SEZER Mehmet FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. Mathematical and Computational Applications, vol.18, no.3, 2013, ss.448 - 458.
AMA	KURT A,YALÇINBAŞ S,SEZER M FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. Mathematical and Computational Applications. 2013; 18(3): 448 - 458.
Vancouver	KURT A,YALÇINBAŞ S,SEZER M FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS. Mathematical and Computational Applications. 2013; 18(3): 448 - 458.
IEEE	KURT A,YALÇINBAŞ S,SEZER M "FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS." Mathematical and Computational Applications, 18, ss.448 - 458, 2013.
ISNAD	KURT, Ayşe vd. "FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS". Mathematical and Computational Applications 18/3 (2013), 448-458.