Stability of 2h-step spline method for delay differential equations

References

• Deiver , R. D. 1977 . Ordinary and delay differential equations , Berlin : Springer .
   Google Scholar
• Hale , J. 1977 . Theory of functional differential equations , Berlin : Springer .
   Google Scholar
• Meinardus , G. and Nurnberger , G. 1985 . International Symposium at University of Monnhein . Delay equations, approximation and application . October 8-11 1985 . Editor
   Google Scholar
• Oberle , H. J. and Pesh , H. J. 1981 . Numerical treatment of delay differential equations by Hermite interpolation . Numer. Math. , 37 : 235 – 255 .
   Web of Science ®Google Scholar
• Arnt , H. 1984 . Numerical solution of retarded initial-value problems: Local and globle error and stepsize control . Numer. Math. , 43 : 343 – 360 .
   Google Scholar
• Bellen , A. 1984 . One-step collection for delay differential equations . J. Comp. App. Math. , 10 : 275 – 283 .
   Web of Science ®Google Scholar
• El-Safty , A. and Abo-Hasha , S. M. 1990 . On the application of spline function to initial- value problems with retarded argument . Intern. J. Computer Math. , 32 : 173 – 179 .
   Web of Science ®Google Scholar
• Abo-Hasha S. M. Numerical solution of delay differential and neutral differential equations using spline methods, Ph.D. Thesis, Assiut University Assiut, Egypt 1993
   Google Scholar
• Loscalzo , F. R. and Talpot , T. D. 1967 . Spline function approximation for solution of ordinary differential equations . SIAM J. Numer. Anal. , 4 ( 3 ) : 433 – 445 .
   Google Scholar
• Ibrahim , M. A.-K. , El-Safty , A. and Abo-Hasha , S. M. 1994 . On the P-stability of quadratic spline delay differential equations . Intern. J. Computer Math. , 52 : 219 – 223 .
   Web of Science ®Google Scholar
• Ibrahim , M. P.-K. , El-Safty , A. and Abo-Hasha , S. M. 1995 . 2h-Step spline method for the solution of delay differential equations . Computer Math. Applic. , 29 ( 8 ) : 1 – 6 .
   Web of Science ®Google Scholar
• Borwell , V. K. 1975 . Special stability problems for functional differential equations . BIT , 15 : 130 – 135 .
   Google Scholar
• Bellman , R. and Cook , K. L. 1963 . Differential-difference equations , New York, London : Academic Press .
   Google Scholar
• Wiederholt , L. F. 1974 . Stability of multistep methods for delay-differential equations . Math. Comput. , 30 : 283 – 290 .
   Google Scholar
• Cryer , C. W. 1974 . Highly stable multistep methods for retarded differential equations . SIAM J. Numer. Anal. , 11 : 788 – 797 .
   Web of Science ®Google Scholar
• Van Der Houwen , P. J. and Sommeijer , B. P. 1984 . Stability in linear multistep method for pure delay equations . J. Comput. Appl. Math. , 10 : 55 – 63 .
   Web of Science ®Google Scholar
• Morden M. The geometry of the zeros of polynomial in a complex variable American Math Society New York. 1949
   Google Scholar