THE APPROXIMATE SOLUTION OF HIGH-ORDER LINEAR DELAY EQUATIONS WITH VARIABLE COEFFICIENTS IN TERMS OF SHIFTED CHEBYSHEV POLYNOMIALS

Abstract

This paper presents a numerical method for the approximate solution of m.th-order linear delay equations with variable coefficients under the mixed conditions in terms of shifted Chebyshev polynomials. The technique we have used is an improved Chebyshev collocation method. In addition, examples that illustrate the pertinent features of the method are presented and the results of study are discussed.

Keywords

• Ötelenmiş Chebyshev polinomları ve serileri, delay denklemleri, Chebshev sıralama yöntemi

References

1. Arıkoglu, A. and Özkol, I., (2006). Solution of difference equations by using differential transform method, Appl. Math.Comput. 174,1216–1228.
2. Derfel, D. (1980). On compactly supported solutions of a class of functional- differential Equations, in “Modern Problems of Function Theory and Functional Analysis”, Karaganta Univ. Press.
3. El-Safty, A. and Abo-Hasha, S.M. (1990). On the application of spline functions to initial value problems with retarded argument, Int. J. Comput. Math. 32,173-179.
4. El-Safty, A., Salim, M.S. and El-Khatib, M.A. (2003). Convergence of the spline function for delay dynamic system, Int. J. Comput. Math. 80,4, 509-518.
5. Fox, L., Mayers, D.F., Ockendon, J.R. and Tayler,A.B.,(1971). On a functional differential equation, J. Inst. Math. Appl. 8,271–307.
6. Gulsu,M. and Sezer,M. (2005). A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math. 82,5,629-642.
7. Gulsu, M. and Sezer, M., (2005). Polynomial solution of the most general linear Fredholm integrodifferential-difference equations by means of Taylor matrix method, Complex Variables,50,5,367-382.
8. Kanwal,R.P.,Liu, K.C. (1989). A Taylor expansion approach for solving integral equation. Int. J.Math.Educ.Sci.Technol.20,3,411-414

9. Karakoç, F.,Bereketoğlu,H. (2009). Solutions of delay differential equations by using differential Transform method, Int. J. Comput. Math. 86,914- 923
10. Nas, Ş., Yalçınbaş, S. and Sezer, M. (2000), A Taylor polynomial approach for solving high- order linear Fredholm integro-differential equations, Int. J. Math. Educ. Sci. Technol. 31,2,213-225.
11. Ocalan, O., Duman, O. (2009). Oscillation analysis of neutral difference equations with delays, Chaos, Solitons & Fractals 39,1,261-270.
12. Parand, K., and Razzaghi, M. (2004). Rational Chebyshev tau method for solving higher-order ordinary differential equations, Int.J.Comput.Math. 81, 73-80
13. Sezer, M. (1996). A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J.Math.Educ. Sci. Technol.27, 6,821-834.
14. Sezer, M., Kaynak,M. (1996). Chebyshev polynomial solutions of linear differential equations, Int. J.Math.Educ. Sci. Technol.27,4,607-618.
15. Sezer, M.,Doğan,S.,(1996). Chebyshev series solutions of Fredholm integral equations, Int. J.Math.Educ. Sci. Technol.27,5,649-657.
16. Synder, M.A.,(1966),Chebyshev methods in Numerical Approximation, Prentice Hall, Inc., London.
17. Xiong, M. and Liang,J. (2007). Novel stability criteria for neutral systems with multiple time delays, Chaos, Solitons & Fractals 32, 1735–1741.
18. Tang, X.H., Yu, J.S. and Peng, D.H. (2000), Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients, Comput. Math. Appl. 39, 169–181.
19. Wei, Z., (2008).Invariant and attracting sets of impulsive delay difference equations with continuous variables, Comp.and Math. with Appl.55,12,2732-2739
20. Zhou, J., Chen, T., and Xiang, L., (2006). Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos, Solitons & Fractals 27,905–913.
21. Zhang, Q., Wei,X., and Xu,J.,(2006). Stability analysis for cellular neural networks with variable delays, Chaos, Solitons & Fractals 28,331–336. ****