308
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

A new Chebyshev polynomial approximation for solving delay differential equations

, &
Pages 1043-1065 | Received 18 Aug 2010, Accepted 01 Dec 2010, Published online: 16 Jun 2011

References

  • Ablowitz , M.J. and Ladik , J.F. 1976 . A nonlinear difference scheme and inverse scattering . Stud. Appl. Math. , 55 : 213 – 229 .
  • Arikoglu , A. and Özkol , I. 2006 . Solution of difference equations by using differential transform method . Appl. Math. Comput. , 174 : 1216 – 1228 .
  • Dai , C. and Zhang , J. 2006 . Jacobian elliptic function method for nonlinear differential-difference equations . Chaos, Soliton Fractals , 27 : 1042 – 1047 .
  • Elmer , C.E. and van Vleck , E.S. 2001 . Travelling wave solutions for bistable differential-difference equations with periodic diffusion . SIAM J. Appl. Math. , 61 : 1648 – 1679 .
  • Elmer , C.E. and van Vleck , E.S. 2002 . A variant of Newton's method for solution of traveling wave solutions of bistable differential-difference equation . J. Dyn. Differ. Equ. , 14 : 493 – 517 .
  • Fan , E. 2001 . Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation . Phys. Lett. A , 282 : 18 – 22 .
  • Gulsu , M. and Sezer , M. 2005 . A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials . Int. J. Comput. Math. , 82 ( 5 ) : 629 – 642 .
  • Gulsu , M. and Sezer , M. 2005 . Polynomial solution of the most general linear Fredholm integrodifferential-difference equations by means of Taylor matrix method . Complex Var. , 50 ( 5 ) : 367 – 382 .
  • Hu , X.B. and Ma , W.X. 2002 . Application of Hirota's bilinear formalism to the Toeplitz lattice some special soliton-like solutions . Phys. Lett. A , 293 : 161 – 165 .
  • Kadalbajoo , M.K. and Sharma , K.K. 2004 . Numerical analysis of singularly perturbed delay differential equations with layer behavior . App. Math. Comput. , 157 : 11 – 28 .
  • Kanwal , R.P. and Liu , K.C. 1989 . A Taylor expansion approach for solving integral equation . Int. J. Math. Educ. Sci. Technol. , 20 ( 3 ) : 411 – 414 .
  • Karakoç , F. and Bereketoğlu , H. 2009 . Solutions of delay differential equations by using differential transform method . Int. J. Comput. Math. , 86 : 914 – 923 .
  • Nas , Ş. , Yalçınbaş , S. and Sezer , M. 2000 . A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations . Int. J. Math. Educ. Sci. Technol. , 31 ( 2 ) : 213 – 225 .
  • Saaty , T.L. 1981 . Modern Nonlinear Equations , 225 New York : Dover Publications, Inc. .
  • Sezer , M. 1996 . A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials . Int. J. Math. Educ. Sci. Technol. , 27 ( 6 ) : 821 – 834 .
  • Synder , M.A. 1966 . “ Chebyshev methods ” . In Numerical Approximation , 256 London : Prentice Hall, Inc. .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.