Approximate solution of generalized pantograph equations withvariable coefficients by operational method

Yalçın ÖZTÜRK, (Muğla Sıtkı Kocman Üniversitesi, Ali Koçman Meslek Yüksekokulu, Muğla, Türkiye)
Mustafa GÜLSU (Muğla Sıtkı Koçman Üniversitesi, Fen Fakültesi,Matematik Bölümü, Muğla, Türkiye)
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
1 0
Yıl: 2017 Cilt: 7 Sayı: 1 Sayfa Aralığı: 66 - 74 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Approximate solution of generalized pantograph equations withvariable coefficients by operational method

Öz:
In this paper, we present an efficient direct solver for solvingthe generalizedpantograph equations with variable coefficients. An approachis based on thesecond kind Chebyshev polynomials together with operational method. Themain characteristic behind this approach is that it reducessuch problem to onesof solving systems of algebraic equations. Only a small number ofChebyshevpolynomials are needed to obtain a satisfactory result. Numerical results withcomparisons are given to confirm the reliability of the proposed method forsolving generalized pantograph equations with variable coefficients.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Ockendon, J.R. and Tayler, A.B., The dynamics of a current collection system for an electric lo- comotive. Proc. Roy. Soc. London, Ser. A, 322, 447-468 (1971).
  • Tayler, A.B., Mathematical Models in Applied Mathematics. Clarendon Press, Oxford, (1986).
  • Ajello, W.G., Freedman, H.I. and Wu, J., Analy- sis of a model representing stage-structured pop- ulation growth with state-dependent time delay. SIAM J. Appl. Math., 52, 855-869 (1992).
  • Buhmann, M.D. and Iserles, A., Stability of the discretized pantograph differential equation. Math. Comput., 60, 575-589 (1993).
  • Derfel, G., On compactly supported solutions of a class of functional-differential equations, in Modern Problems of Function Theory and Functional Analysis. Karaganda University Press, Kazakhstan, (1980).
  • Feldstein, A. and Liu, Y., On neutral functional- differential equations with variable time delays. Math. Proc. Camb. Phil. Soc., 124, 371-384 (1998).
  • Derfeland, G. and Levin, D., Generalized refine- ment equation and subdivision process. J. Approx. Theory, 80, 272-297 (1995).
  • Sezer, M. and Akyuz, A., A Taylor method for nu- merical solution of generalized pantograph equa- tion with linear functional argument. J. Comp. Appl. Math., 200, 217-225 (2007).
  • Sezer, M., Yalnbas, S. and Sahin, N., Approxi- mate solution of multi-pantograph equation with variable coefficients. J. Comp. Appl. Math., 214, 406-416 (2008).
  • Saadatmandi, A. and Dehghan, M., Variational iteration method for solving a generalized pantgo- raph equation. Comp. Math. Appl., 58, 2190-2196 (2009).
  • Evans, D.J. and Raslan, K.R., The Adomian de- composition method for solving delay differen- tial equation. Int. J. Comp. Math., 82(1), 49-54 (2005).
  • Buhmann, M. and Iserles, A., Stability of the discretized pantograph differential equation. J. Math. Comp., 60, 575-589 (2005).
  • Li, D. and Liu, M.Z., Runge-Kutta methods for the multi-pantograph delay equation. Appl. Math. Comp., 163, 383-395 (2005).
  • Shakeri, F. and Dehghan, M., Solution of the de- lay differential equations via homotopy perturba- tion method. Math. Comp. Modelling, 48, 486-498 (2008).
  • Muroya, Y., Ishiwata, E. and Brunner, E., On the attainable order of collocation methods for pan- tograph integro-differential equations. J. Comp. Appl. Math., 152, 347-366 (2003).
  • Huan-Yu, Z., Variational iteration method for solving the multi-pantograph delay equation. Physics Letter A, 372 (43), 6475-6479 (2008).
  • Sezer, M. and Gulsu, M., A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument. Appl. Math. Comp., 171, 332-344 (2005).
  • Ping Yang, S. and Xiao, A.G., Convergence of the variational iteration method for solving multi- delay differential equaitons. Comp. Math. Appl., 61(8), 2148-2151 (2011).
  • Liu, M.Z. and Li, D., Properties of analitic solu- tion and numerical solution of multi-pantograph equation. Appl. Math. Comp., 155, 853-871 (2004).
  • Yusufoglu, E., An efficint algorithm for solving generalized pantograph equation with linear func- tional argument. Appl. Math. Comp., 217, 3591- 3595 (2010).
  • El-Safty, Salim, M.S. and El-Khatib, M.A., Con- vergence of the spline function for delay dy- namic system. Int. J. Comp. Math., 80(4),509-518 (2004).
  • Fox, L. and Parker, I.B., Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London, (1968).
  • Mason, J.C. and Handscomb, D.C., Chebyshev polynomials. Chapman and Hall/CRC, New York, (2003).
  • Body, J.P., Chebyshev and fourier spectral meth- ods, University of Michigan, New York, (2000).
  • Saadatmandi, A. and Dehghan, M., Numerical solotion of hyperbolic telegraph equation using the Chebshev tau method. Numer. Meth. Partial Diff. Equations, 26, 239-252 (2010).
  • Lakestani, M. and Dehghan, M., Numerical solu- tion of Riccati equation using the cubic B spline scaling functions and Chebyshev cardinal func- tions. Comp. Physics Communications, 181, 957- 966 (2010).
  • Lakestani M. and Dehghan, M., Numerical so- lution of fourth order integro differential equa- tions using Chebyshev cardinal functions. Inter. J. Com. Math., 87, 1389-1394 (2010).
  • Saadatmandi, A. and Dehghan, M., The numer- ical solution of problems in calculus of variation using Chebyshev finite difference method. Physi. Letter A, 22, 4037-4040 (2008).
  • Pandey, R.K. and Kumar, N., Solution of Lane- Emden type equations using Berstein operational matrix of differentiation. New Astronomy, 17, 303- 308 (2012).
  • Saadatmandi, A. and Dehghan, M., A new apera- tional matrix for solving fractional-order differen- tial equations. Comp. Math. Appl., 59, 1326-1336 (2010).
  • Parand, K. and Razzaghi, M., Rational Cheby- shev tau method for solving higher-order ordinary differential equations. Int. J. Comput. Math., 81, 73-80 (2004).
  • Razzaghi, M. and Yousefi, S., Legendre wavelets operational matrix of integration. Int. J. Syst. Sci., 32(4), 495-502 (2001).
  • Babolian E. and F. Fattahzadeh, Numerical solu- tion of differential equations by using Chebyshev wavelet operational matrix of integration. Appl. Math. Comp., 188, 417-425 (2007).
  • Rao G.P. and Palanisamy, K.R., Walsh stretch matrices and functional differential equations. IEEE Trans. Autom. Control, 27, 272-276 (1982).
  • Hwang, C., Solution of a functional differential equation via delayed unit step functions. Int. J. Syst. Sci., 14(9), 1065-1073 (1983).4
  • Hwang, C. and Shih, Y.P., Laguerre series solu- tion of a functional differential equation. Int. J. Syst. Sci., 13(7), 783-788 (1982).
APA ÖZTÜRK Y, GÜLSU M (2017). Approximate solution of generalized pantograph equations withvariable coefficients by operational method. , 66 - 74.
Chicago ÖZTÜRK YALÇIN,GÜLSU MUSTAFA Approximate solution of generalized pantograph equations withvariable coefficients by operational method. (2017): 66 - 74.
MLA ÖZTÜRK YALÇIN,GÜLSU MUSTAFA Approximate solution of generalized pantograph equations withvariable coefficients by operational method. , 2017, ss.66 - 74.
AMA ÖZTÜRK Y,GÜLSU M Approximate solution of generalized pantograph equations withvariable coefficients by operational method. . 2017; 66 - 74.
Vancouver ÖZTÜRK Y,GÜLSU M Approximate solution of generalized pantograph equations withvariable coefficients by operational method. . 2017; 66 - 74.
IEEE ÖZTÜRK Y,GÜLSU M "Approximate solution of generalized pantograph equations withvariable coefficients by operational method." , ss.66 - 74, 2017.
ISNAD ÖZTÜRK, YALÇIN - GÜLSU, MUSTAFA. "Approximate solution of generalized pantograph equations withvariable coefficients by operational method". (2017), 66-74.
APA ÖZTÜRK Y, GÜLSU M (2017). Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(1), 66 - 74.
Chicago ÖZTÜRK YALÇIN,GÜLSU MUSTAFA Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no.1 (2017): 66 - 74.
MLA ÖZTÜRK YALÇIN,GÜLSU MUSTAFA Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), vol.7, no.1, 2017, ss.66 - 74.
AMA ÖZTÜRK Y,GÜLSU M Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2017; 7(1): 66 - 74.
Vancouver ÖZTÜRK Y,GÜLSU M Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2017; 7(1): 66 - 74.
IEEE ÖZTÜRK Y,GÜLSU M "Approximate solution of generalized pantograph equations withvariable coefficients by operational method." An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7, ss.66 - 74, 2017.
ISNAD ÖZTÜRK, YALÇIN - GÜLSU, MUSTAFA. "Approximate solution of generalized pantograph equations withvariable coefficients by operational method". An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7/1 (2017), 66-74.
Sayfa Oluşturulma Tarihi
04-05-2024 10:38

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