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Original Articles

Existence, Uniqueness and Applications of the Spline Method for Functional-Differential Equation of Neutral Type

Pages 775-788 | Published online: 15 Sep 2010

  • Casdeton , R. N. and Grimm , L. J. 1973 . A first order method for differential equations of neutral type . Math.Comp. , 27 : 572 – 577 .
  • Grimm , L. J. 1972 . Analytic solutions of a neutral differential equation near a singular point . Proc. Amer. Math. Soc. , 36 : 187 – 190 .
  • Grimm , L. J. 1972 . Existence and continuous dependence for a class of nonlinear neutral differential equations . Plroc. Amer. Math. Soc. , 36 : 187 – 190 .
  • Homung , U. 1975 . Euler-Verfahren fur neutrale Funktional-differential gleichungen” . Numer. Math. , 24 : 233 – 240 .
  • Bainov , D. D. , Myshkis , A. D. and Zahariev , A. I. 1990 . Necessary and sufficient conditions for oscillation of the solutions of linear functional differential equations of neutral type with distributed delay . J. Math. Anal. Appl. , 148 : 263 – 273 .
  • Bellman , R. and Cook , K. L. 1965 . On the computational solution of a class of functional differential equations . J. Math. Anal. Appl. , 12 : 495 – 500 .
  • Zveridna , T. S. 1965 . A modified Adams formula for the integrating of equations with deviating argument(Russian} . Tigumentom Univ. Diuzby Narodov Patrisa Lumumby , 3 : 221 – 232 .
  • Jackiewicz , Z. 1979 . Convergence of multistep methods for voltena functional differential equations . Numer.MaA. , 32 : 307 – 332 .
  • Jackiewicz , Z. 1981 . One-step methods for the numerical solution of voltena functional differential equations ofneutral type . Applicable Anal. , 12 : 1 – 11 .
  • Jackiewicz , Z. 1981 . The numerical solution of voltena functional differential equations of neutral type . SIAMJ. Numer. Anal. , 18 : 615 – 626 .
  • Jackiewicz , Z. 1984 . Adams methods for neutral functional differential equation . Numer. MaA. , 39 : 221 – 230 .
  • Jackiewicz , Z. 1984 . One-step methods of any order for neutral functional differential equations . SIAM J.Numer. Anal. , 21 : 486 – 511 .
  • Gyori , I. 1989 . Oscillation of retarded differential equations of the neutral and the mixed types . J. Math. Anal.Appl. , 141 : 1 – 20 .
  • Driver , R. D. 1965 . Existence and continuous dependence of solutions of a neutral functional differentialequations . Arch. Rational Mech. Anal. , 19 : 149 – 166 .
  • Bellen , A. , Jackiewicz and Zennaro . 1988 . Stability analysis of one-step methods for neutral delay-differentialequations . Numer. Math. , 52 : 605 – 619 .
  • Rappel , F. and Kunisch , K. 1981 . Spline approximations for neutral functional differential equations . SIAMJ.Numer. Anal. , 18 : 1058 – 1080 .
  • Ciyer , C. W. 1972 . Numerical methods for functional differential equations delay and functional differential equations , Edited by: Schnitt , K. 17 – 101 . New York : Academic Press .
  • El-Safty , A. , Salim , M. S. and El-Khatib , M. A. 2000 . Existence, Uniqueness and Stability of the splinefunction for delay controlled dynamic system . Intern. J. Computer Math. , 78 (3-4} )
  • El-Safty , A. and Shadia , M. 1990 . On the application of spline functions to initial value problems with retarded argument . Intern. J. Computer Math. , 32 : 173 – 179 .

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