Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 4, 248 - 260, 01.10.2017

Öz

Kaynakça

  • J.R. Ockendon and A.B. Tayler, The Dynamics of a current collection system for an electric locomotive, Proc R Soc London Ser A 322 (1971), 447-468.
  • G.A. Derfel and F. Vogl, On the asymptotics of solutions of a class of linear functional-differential equations, Eur J Appl Maths 7 (1996),511-518.
  • Feldstein and Y. Liu, On neutral functional-differenrial equations with variable time delays, Math Proc Cambridge Philos Soc 124 (1998), 371-384
  • G.R. Morris, A. Feldstein, and E. W. Bowen, The Phragmen-Lindel’ of principle and a class of functional-differential equations, Proceedings of NRL-MRC Conference on Ordinary Differential Equations, Academic Press, New York,1972,pp. 513-540.
  • G. Derfel and A. Iserles, The pantograph equaiton in the complex plane, J Math Anal Appl 213 (1997),117-132.
  • 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.
  • M. D. Buhmann and A. Iserles, Stability of the discretized pantograph differential equation, Math Comput 60 (1993), 575-589.
  • 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.
  • G. Derfel, On compactly supported solutions of a class of functional-differential equations, Modern problems of functions theory and functional analysis, Karaganda University Press, 1980, (in Russian).
  • G. Derfel, N. Dyn, and D. Levin, Generalized refinement equation and subdivision process, J Approx Theory 80 (1995), 272-297.
  • M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol. 25 (1994) 625-633
  • B. Bülbül, M. Gülsu, M. Sezer, A New Taylor collocation method for nonlinear Fredholm-Volterra integro-differential equations, Numer. Methods for partial Diff. Eq. (2009) doi: 10.1002/num.20470.
  • A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79 (9) (2002) 987-1000.
  • M. Sezer, M. Gülsu, Polynomial solution of the most general linear Fredholm integro-differential-difference equation by means of Taylor matrix method. Int. J. Complex Var. 50 (5) (2005) 367-382
  • N. Kurt and M. Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, J Franklin Inst 345 (2008),839-850.
  • M. Sezer and A. Akyüz-Daşcıoğlu, A Taylor method for numerical solution of generalized pantograph equations with linear functional argument, J Comput Appl Math 200 (2007), 217-225
  • M. Gülsu, Y. Öztürk, M. Sezer, A New collocation method for solution of mixed linear itegro-differential-difference equations, Appl. Math. Comput.(2010), in press, doi:10.1016/j.amc.2010.03.054.
  • Ş. Yüzbaşı, Bessel polynomial solutions of linear differential, integral and integro- differential equations, MSc Thesis, Graduate School of Natural and Applied Sciences, Muğla Uni.,2009.
  • M. Z. Liu and D. Li, Properties of analytic solution and numerical solution and multi-pantograph equation, Appl Math Comput 155 (2004), 853-871.
  • D. J. Evans and K. R. Raslan, The Adomain decomposition method for solving delay differential equation, Int J Comput Math 82 (2005), 49-54.
  • Y. Muroya, E. Ishiwata, and H. Brunner, On the attainable order of collocation methods for pantograph integro-differential equations, J Comput Appl Math 152 (2003),347-366.
  • A. Akyüz-Daşçıoğlu and H. Ç. Yaslan, An approximation method for solution of nonlinear integral equations, Appl. Math. Comput. 174 (2006) 619-629.
  • F.A. Oliveira, Collocation and residual correction, Numer. Math. 36 (1980) 27-31.
  • İ. Çelik, Approximate calculation of eigenvalues with the method of weighted residuals-colllocation method, Appl. Math. Comput. 160 (2005) 401-410.
  • S. Shahmorad, Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation, Appl. Math. Comput. 167 (2005) 1418-1429
  • İ. Çelik, Collocation method and residual correction using Chebyshev series, Appl. Math. Comput. 174 (2006) 910-920.

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

Yıl 2017, Cilt: 5 Sayı: 4, 248 - 260, 01.10.2017

Öz

In this article, an improved collocation method based on the Morgan-Voyce polynomials for the approximates solution of multi-pantograph equations is introduced. The method is based upon the improvement of Morgan-Voyce polynomial solutions with the aid of the residual error function. First, the Morgan-Voyce collocation method is applied to the multi-pantograph equations and then Morgan-Voyce polynomial solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Morgan-Voyce collocation method. By summing the Morgan-Voyce polynomial solutions of the original problem and the error problem, we have the improved Morgan-Voyce polynomial solutions. When the exact solution of problem is not known, the absolute error can then be approximately computed by the Morgan-Voyce polynomial solution of the error problem. Numerical examples that the pertinent features of the method are presented. We have applied all of the numerical computations on computer using a program written in MATLAB.

Kaynakça

  • J.R. Ockendon and A.B. Tayler, The Dynamics of a current collection system for an electric locomotive, Proc R Soc London Ser A 322 (1971), 447-468.
  • G.A. Derfel and F. Vogl, On the asymptotics of solutions of a class of linear functional-differential equations, Eur J Appl Maths 7 (1996),511-518.
  • Feldstein and Y. Liu, On neutral functional-differenrial equations with variable time delays, Math Proc Cambridge Philos Soc 124 (1998), 371-384
  • G.R. Morris, A. Feldstein, and E. W. Bowen, The Phragmen-Lindel’ of principle and a class of functional-differential equations, Proceedings of NRL-MRC Conference on Ordinary Differential Equations, Academic Press, New York,1972,pp. 513-540.
  • G. Derfel and A. Iserles, The pantograph equaiton in the complex plane, J Math Anal Appl 213 (1997),117-132.
  • 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.
  • M. D. Buhmann and A. Iserles, Stability of the discretized pantograph differential equation, Math Comput 60 (1993), 575-589.
  • 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.
  • G. Derfel, On compactly supported solutions of a class of functional-differential equations, Modern problems of functions theory and functional analysis, Karaganda University Press, 1980, (in Russian).
  • G. Derfel, N. Dyn, and D. Levin, Generalized refinement equation and subdivision process, J Approx Theory 80 (1995), 272-297.
  • M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol. 25 (1994) 625-633
  • B. Bülbül, M. Gülsu, M. Sezer, A New Taylor collocation method for nonlinear Fredholm-Volterra integro-differential equations, Numer. Methods for partial Diff. Eq. (2009) doi: 10.1002/num.20470.
  • A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79 (9) (2002) 987-1000.
  • M. Sezer, M. Gülsu, Polynomial solution of the most general linear Fredholm integro-differential-difference equation by means of Taylor matrix method. Int. J. Complex Var. 50 (5) (2005) 367-382
  • N. Kurt and M. Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, J Franklin Inst 345 (2008),839-850.
  • M. Sezer and A. Akyüz-Daşcıoğlu, A Taylor method for numerical solution of generalized pantograph equations with linear functional argument, J Comput Appl Math 200 (2007), 217-225
  • M. Gülsu, Y. Öztürk, M. Sezer, A New collocation method for solution of mixed linear itegro-differential-difference equations, Appl. Math. Comput.(2010), in press, doi:10.1016/j.amc.2010.03.054.
  • Ş. Yüzbaşı, Bessel polynomial solutions of linear differential, integral and integro- differential equations, MSc Thesis, Graduate School of Natural and Applied Sciences, Muğla Uni.,2009.
  • M. Z. Liu and D. Li, Properties of analytic solution and numerical solution and multi-pantograph equation, Appl Math Comput 155 (2004), 853-871.
  • D. J. Evans and K. R. Raslan, The Adomain decomposition method for solving delay differential equation, Int J Comput Math 82 (2005), 49-54.
  • Y. Muroya, E. Ishiwata, and H. Brunner, On the attainable order of collocation methods for pantograph integro-differential equations, J Comput Appl Math 152 (2003),347-366.
  • A. Akyüz-Daşçıoğlu and H. Ç. Yaslan, An approximation method for solution of nonlinear integral equations, Appl. Math. Comput. 174 (2006) 619-629.
  • F.A. Oliveira, Collocation and residual correction, Numer. Math. 36 (1980) 27-31.
  • İ. Çelik, Approximate calculation of eigenvalues with the method of weighted residuals-colllocation method, Appl. Math. Comput. 160 (2005) 401-410.
  • S. Shahmorad, Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation, Appl. Math. Comput. 167 (2005) 1418-1429
  • İ. Çelik, Collocation method and residual correction using Chebyshev series, Appl. Math. Comput. 174 (2006) 910-920.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Ozgul Ilhan Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 4

Kaynak Göster

APA Ilhan, O. (2017). An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations. New Trends in Mathematical Sciences, 5(4), 248-260.
AMA Ilhan O. An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations. New Trends in Mathematical Sciences. Ekim 2017;5(4):248-260.
Chicago Ilhan, Ozgul. “An Improved Morgan-Voyce Collocation Method for Numerical Solution of Multi-Pantograph Equations”. New Trends in Mathematical Sciences 5, sy. 4 (Ekim 2017): 248-60.
EndNote Ilhan O (01 Ekim 2017) An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations. New Trends in Mathematical Sciences 5 4 248–260.
IEEE O. Ilhan, “An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations”, New Trends in Mathematical Sciences, c. 5, sy. 4, ss. 248–260, 2017.
ISNAD Ilhan, Ozgul. “An Improved Morgan-Voyce Collocation Method for Numerical Solution of Multi-Pantograph Equations”. New Trends in Mathematical Sciences 5/4 (Ekim 2017), 248-260.
JAMA Ilhan O. An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations. New Trends in Mathematical Sciences. 2017;5:248–260.
MLA Ilhan, Ozgul. “An Improved Morgan-Voyce Collocation Method for Numerical Solution of Multi-Pantograph Equations”. New Trends in Mathematical Sciences, c. 5, sy. 4, 2017, ss. 248-60.
Vancouver Ilhan O. An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations. New Trends in Mathematical Sciences. 2017;5(4):248-60.