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

Ali Fuat Yeniçerioğlu; Ali Fuat Yeniçerioğlu; Barış Demir

Research Article

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

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

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.

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

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.

There are 14 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Articles
Authors	Ali Fuat Yeniçerioğlu Ali Fuat Yeniçerioğlu Barış Demir This is me
Publication Date	May 6, 2015
Published in Issue	Year 2012 Volume: 5 Issue: 1-2

Cite

APA	Yeniçerioğlu, A. F., Yeniçerioğlu, A. F., & Demir, B. (2015). ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION". Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 5(1-2), 109-129.
AMA	Yeniçerioğlu AF, Yeniçerioğlu AF, Demir B. ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION". BUJSE. May 2015;5(1-2):109-129.
Chicago	Yeniçerioğlu, Ali Fuat, Ali Fuat Yeniçerioğlu, and Barış Demir. “ON THE STABILITY OF SECOND ORDER ‘NEUTRAL DELAY DIFFERANTIAL EQUATION’”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 5, no. 1-2 (May 2015): 109-29.
EndNote	Yeniçerioğlu AF, Yeniçerioğlu AF, Demir B (May 1, 2015) ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION". Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5 1-2 109–129.
IEEE	A. F. Yeniçerioğlu, A. F. Yeniçerioğlu, and B. Demir, “ON THE STABILITY OF SECOND ORDER ‘NEUTRAL DELAY DIFFERANTIAL EQUATION’”, BUJSE, vol. 5, no. 1-2, pp. 109–129, 2015.
ISNAD	Yeniçerioğlu, Ali Fuat et al. “ON THE STABILITY OF SECOND ORDER ‘NEUTRAL DELAY DIFFERANTIAL EQUATION’”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5/1-2 (May 2015), 109-129.
JAMA	Yeniçerioğlu AF, Yeniçerioğlu AF, Demir B. ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION". BUJSE. 2015;5:109–129.
MLA	Yeniçerioğlu, Ali Fuat et al. “ON THE STABILITY OF SECOND ORDER ‘NEUTRAL DELAY DIFFERANTIAL EQUATION’”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 5, no. 1-2, 2015, pp. 109-2.
Vancouver	Yeniçerioğlu AF, Yeniçerioğlu AF, Demir B. ON THE STABILITY OF SECOND ORDER "NEUTRAL DELAY DIFFERANTIAL EQUATION". BUJSE. 2015;5(1-2):109-2.