ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION"

Year 2012, Volume: 5 Issue: 1-2, 109 - 129, 06.05.2015

Ali Fuat Yeniçerioğlu , Ali Fuat Yeniçerioğlu , Barış Demir

https://izlik.org/JA67EZ42UD

Abstract

On the stability of second order neutral delay differential equation;
In this paper, a basic theorem on the behavior of solutions of linear
second order neutral delay differential equation is established. As
a consequence of this theorem, a stability criterion is obtained. 

Keywords

"Neutral delay" differential equation , Characteristic equation , Stability , Trivial solution

ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION"

https://izlik.org/JA67EZ42UD

Abstract

İkinci mertebeden neutral delay diferansiyel denklemlerin
kararlılığı: Bu makalede sabit katsayılı doğrusal ikinci mertebeden
neutral delay diferansiyel denklemlerin davranışları üzerinde temel
bir teorem verilmiştir. Bu teoremin sonuçlarından yararlanarak
kararlılık kriterleri elde edilmiştir.

Keywords

"Neutral delay" differansiyel denklemi , karakteristik denklem , kararlılık , aşikar çözüm

References

• R. Bellman, and K. Cooke, Differential-Difference Equations. Academic Press, New York, (1963).
• B. Cahlon and D. Schmidt, Stability criteria for certain secondorder delay differential equations with mixed coefficients, Journal of Computational and Applied Mathematics, 170 (2004) 79-102.
• R.D. Driver, Exponential decay in some linear delay differential equations, JSTOR: American Mathematical Monthly: vol. 85, No.9, (1978) 757-760.
• R.D. Driver, Ordinary and Delay Differential Equations, Appl. Math. sciences 20, Springer, Berlin, 1977.
• El'sgol'ts L.E. and Norkin S.B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Pres, New York, London, 1973.
• J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, 1993.
• G.D. Hu and T. Mitsui, Stability of numerical methods for system of neutral delay differential equations, BIT Numerical Mathematics, 35 (1995) 505-515.
• V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, 1992.
• I.-G.E. Kordonis and Ch.G. Philos, The Behavior of solutions of linear integro-differential equations with unbounded delay, Computers & Mathematics with Applications, 38 (1999) 45-50.
• N. Macdonald, Biological Delay Systems: Linear Stability Theory, Cambridge University Pres, Cambridge, New York, 1989.
• Ch.G. Philos and I.K. Purnaras, Periodic first order linear neutral delay differential equathons, Applied Mathematics and Computation,117 (2001) 203-222.
• C.R. Steele, Studies of the ear, Lectures in Applied Mathematics, Vol.17, American Mathematical Society, RI, 1979, pp. 69-71.
• S.A. Tobias, Machine Tool Vibrations, Blackie, London, 1965.
• S. Yal9inba§, F. Yeni9erioglu, Exact and Approximate Solutions of Second Order Including Function Delay Differential Equations with Variable Coefficients, Applied Mathematics and Computation, vol:148, (2004), 287-298.