Öz
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.
Anahtar Kelimeler
"Neutral delay" differential equation Characteristic equation Stability Trivial solution
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
"Neutral delay" differansiyel denklemi karakteristik denklem kararlılık aşikar çözüm
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Mayıs 2015 |
| Yayımlandığı Sayı | Yıl 2012 Cilt: 5 Sayı: 1-2 |
Kaynak Göster
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