A collocation method using Hermite polynomials for approximate solution of pantograph equations

Journal of the Franklin Institute

Volumn 348, Issue 6, 2011, Pages 1128-1139

  Yalçinbaç, Salih ^a   Aynigül, Müge ^a   Sezer, Mehmet ^b  

^a CELAL BAYAR UNIVERSITY   (Turkey)

^b MUGLA SITKI KOCMAN UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE SOLUTION; COLLOCATION METHOD; HERMITE POLYNOMIALS; INITIAL CONDITIONS; NUMERICAL EXAMPLE; PANTOGRAPH EQUATION; VARIABLE COEFFICIENTS;

PANTOGRAPHS; POLYNOMIAL APPROXIMATION;

NUMERICAL METHODS;

EID: 79957616126     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2011.05.003     Document Type: Article

References (22)

1. J.R. Ockendon, and A.B. Tayler The dynamics of a current collection system for an electric locomotive Proc. Roy. Soc. London A 322 1971 447 468
2. G.A. Derfel, and F. Vogl On the asymptotics of solutions of a class of linear functionaldifferential equations, Eur. J. Appl. Math. 7 1996 511 518 (Pubitemid 126416031)
3. G.R. Morris, A. Feldstein, E.W. Bowen, The PhragmenLindel of principle and a class of functionaldifferential equations, in: Proceedings of the NRLMRC Conference on Ordinary Differential Equations, 1972, pp. 513540.
4. G. Derfel, and A. Iserles The pantograph equation in the complex plane J. Math. Anal. Appl. 213 1997 117 132 (Pubitemid 127170205)
5. G. Derfel On compactly supported solutions of a class of functionaldifferential equations Modern Problems of Functions Theory and Functional Analysis 1980 Karaganda University Press (in Russian)
6. G. Derfel, N. Dyn, and D. Levin Generalized refinement equation and subdivision process J. Approx. Theory 80 1995 272 297
7. L. Fox, D.F. Mayers, J.A. Ockendon, and A.B. Tayler On a functional differential equation J. Inst. Math. Appl. 8 1971 271 307
8. W.G. Ajello, H.I. Freedman, and J. Wu A model of stage structured population growth with density depended time delay SIAM J. Appl. Math. 52 1992 855 869
9. M.D. Buhmann, and A. Iserles Stability of the discretized pantograph differential equation Math. Comput. 60 1993 575 589
10. M. Gülsu, and M. Sezer The approximate solution of high-order linear difference equation with variable coefficients in terms of Taylor polynomials Appl. Math. Comput. 168 1 2005 76 88 (Pubitemid 41383644)
11. M. Gülsu, and M. Sezer A Taylor polynomial approach for solving differential-difference equations J. Comput. Appl. Math. 186 2 2006 349 364 (Pubitemid 41433589)
12. R.P. Kanwal, and K.C. Liu A Taylor expansion approach for solving integral equations Int. J. Math. Educ. Sci. Technol. 20 3 1989 411 414
13. Nas, S. Yalçnba, and M. Sezer A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations Int. J. Math. Educ. Sci. Technol. 31 2 2000 213 225
14. M. Sezer A method fort he approximate solution of the second order linear differential equations in terms of Taylor polynomials Int. J. Math. Educ. Sci. Technol. 27 6 1996 821 834 (Pubitemid 126156135)
15. M. Sezer, and M. Gülsu A new polynomial approach for solving difference and Fredholm integro-difference equation with mixed argument Appl. Math. Comput. 171 1 2005 332 344 (Pubitemid 41737305)
16. S. Yalçnba, and M. Sezer The approximate solution of high-order linear VolterraFredholm integro-differential equations in terms of Taylor polynomials Appl. Math. Comput. 112 2000 291 308
17. M. Sezer, S. Yalçnba, and N. ahin Approximate solution of multi-pantograph equation with variable coefficients J. Comput. Appl. Math. 214 2008 406 416 (Pubitemid 351241078)
18. M.Z. Liu, and D. Li Properties of analytic solution and numerical solution and multi-pantograph equation Appl. Math. Comput. 155 2004 853 871
19. D.J. Evans, and K.R. Raslan The adomain decomposition method for solving delay differential equation Int. J. Comput. Math. 82 1 2005 49 54 (Pubitemid 41663479)
20. M. Sezer, and A. Akyüz-Dacolu A Taylor method for numerical solution of generalized pantograph equations with linear functional argument 200 2007 217 225
21. G.P. Rao, and K.R. Palanisamy Walsh stretch matrices and functional differential equation IEEE Trans. Autom. Control 27 1982 272 276
22. C. Hwang, and Y.P. Shih Laguerre series solution of a functional differential equation Int. J. Syst. Sci. 13 7 1982 783 788