Numerical Approximation of Neutral Differential Equations on Infinite Interval

References

• Cooke , K. L. and Györi , I. 1994 . Numerical approximation of the solutions of delay differentialequations on an infinite interval using piecewise constant arguments . Comput. Math.Appl , 28 (1-3) : 81 – 92 .
   Web of Science ®Google Scholar
• Cooke , K. L. and Wiener , J. 1984 . Retarded differential equations with piecewise constant delays . J. Math. Anal Appl , 99 : 265 – 297 .
   Web of Science ®Google Scholar
• Cooke , K. L. and Wiener , J. 1986 . Stability regions for linear equations with piecewise continuousdelays . Comput. Math. Appl , 12A : 695 – 701 .
   Google Scholar
• Cooke , K. L. and Wiener , J. 1991 . “ A Survey of Differential Equations with Pecewise ContinuousArguments ” . In Delay Differential Equations andDynamical Systems , Lecture Notes in Math Edited by: Busenberg , S. and Martelli , M. Vol. 1475 , 1 – 15 . Berlin : Springer .
   Google Scholar
• Gopalsamy , K. 1992 . Stability and Oscillation in Delay Differential Equations of PopulationDynamics , Boston : Kluwer .
   Google Scholar
• Gyori , I. 1991 . On approximation of the solutions of delay differential equations by usingpiecewise constant arguments . Int. J. Main. Main. Sci. , 14 (1) : 111 – 126 .
   Google Scholar
• Gyori , I. and Hartung , F. 2001 . Stability in delay perturbed differential and difference equations,Topics in Functional Differential and Difference Equations . Fields InstituteCommunications , 29 : 181 – 194 .
   Google Scholar
• Gyori , I. and Hartung , F. 2001 . Preservation of stability in a linear neutral differential equationunder delay perturbation . Dyn. Syst. Appl , 10 : 225 – 242 .
   Google Scholar
• Gyori , I. , Hartung , F. and Turi , J. 1995 . Numerical approximations for a class of differentialequations with time- and state-dependent delays . Appl. Math. Lett. , 8 (6) : 19 – 24 .
   Web of Science ®Google Scholar
• Gyori , I. and Pituk , M. Asymptotic Stability in a Linear Delay Difference Equation . Advances in Difference Equations, Proceedings of theSecond International Conference on Difference Equations . Edited by: Elaydi , S. , Gyori , I. and Ladas , G. Amsterdam : Gordon and Breach .
   Google Scholar
• Hale , J. K. and Verduyn , S. M. 1993 . Lunel, Introduction to Functional Differential Equations , New York : Springer .
   Google Scholar
• Hartung , F. , Herdman , T. L. and Tan , J. Identifications of parameters in hereditary systems: anumerical study . Proceedings of the 3rd IEEE Mediterranean Symposium on NewDirections in Control and Automation . Cyprus . pp. 291 – 298 .
   Google Scholar
• Hartung , F. , Herdman , T. L. and Tan , J. 1997 . On existence, uniqueness and numericalapproximation for neutral equations with state-dependent delays . Appl. Num. Math. , 24 : 393 – 409 .
   Web of Science ®Google Scholar
• Hartung , F. , Herdman , T. L. and Turi , J. 1998 . Parameter identification in classes of hereditarysystems of neutral type . AppL Math. Comp. , 89 (1-3) : 147 – 160 .
   Web of Science ®Google Scholar
• Hartung , F. and Tan , J. 1997 . Identification of parameters in delay equations with state-dependentdelays . Nonlinear AnaL: Theory. Mein. Appl , 29 (11) : 1303 – 1318 .
   Web of Science ®Google Scholar
• Kocic , V. L. and Ladas , G. 1993 . Global Behavior of Nonlinear Difference Equations of HigherOrder with Applications , Dordrecht : Kluwer .
   Google Scholar
• Kovacsvolgyi , I. 2000 . The asymptotic stability of difference equations . AppL Math. Lett. , 13 : 1 – 6 .
   Web of Science ®Google Scholar
• Krisztin , T. 1990 . Stability for functional-differential equations and some variational problems . Tohoku Math. J. , 42 (3) : 407 – 417 .
   Web of Science ®Google Scholar
• Ladas , G. , Qian , C. , Vlahos , P. N. and Yan , J. 1991 . Stability of solutions of linear nonautonomousdifference equations . Appl. Anal. , 41 : 183 – 191 .
   Google Scholar
• Ogita , R. , Matsunaga , H. and Kara , T. 2000 . Asymptotic stability condition for a class of linear delaydifference equations of higher order . J. Math. Anal. Appl. , 248 : 83 – 96 .
   Web of Science ®Google Scholar
• Wiener , J. 1993 . Generalized Solutions of Functional Differential Equations , Singapore : World Scientific .
   Google Scholar
• Yu , J. S. 1996 . Asymptotic stability for nonautonomous scalar neutral differential equations . J. Math. Anal. Appl. , 203 : 850 – 860 .
   Web of Science ®Google Scholar