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Residual correction of the Hermite polynomial solutions of the generalized pantograph equations

Year 2015, Volume: 3 Issue: 2, 118 - 125, 19.01.2015

Şuayip Yüzbaşı Emrah Gök Mehmet Sezer

Abstract

In this paper, we consider the residual correction of the Hermite polynomial solutions of the generalized pantographequations. The Hermite polynomial solutions are obtained by a collocation method. By means of this collocation method, the problemis into a system of algebraic equations and thus unknown coefficients are determined. An error problem is constructed by using theorginal problem and the residual function. Error problem is solved by the Hermite collocation method and thus the imrovedapproximate solutions are gained. The technique is illustrated by studying the problem for two examples. The obtained results showthat the residual corrcetion method is very effective

Keywords

Pantograph equations Hermite polynomials collocation method residual function

References

  • Yusufo˘glu E., An efficient algorithm for solving generalized pantograph equations with linear functional argument, Appl. Math. Comput., 217 (2010) 3591-3595.
  • Sezer M., .Aky¨uz-Das¸cıo˘glu A, A Taylor method for numerical solution of generalized pantograph equations with lineer functional argument, J. Comput. Appl. Math., 200 (2007) 217-225.
  • Yu Z.-H., Variational iteration method for solving the multi-pantograph delay equation, Physics Letters A 372 (2008) 6475-6479.
  • Y¨uzbas¸ı S¸., S¸ahin N., Sezer M., A Bessel collocation method for numerical solution of generalized pantograph equations, Numer Methods Partial Differential Equations 28 (2012) 1105-1123.
  • Liu M.Z., Li D., Properties of analytic solution and numerical solution of multi-pantograph equation, Appl. Math. Comput. 155 (2004) 853-871.
  • Yalc¸ınbas¸ S., Aynig¨ul M., Sezer M., A collocation method using Hermite polynomials for approximate solution of pantograph equations, J. Frank. Inst. 348 (2011) 1128–1139.
  • Saadatmandi A., Dehghan M., Variational iteration method for solving a generalized pantograph equation, Comput. Math. Appl. 58(2009) 2190-2196.
  • Keskin Y., Kurnaz A., Kiris¸ M.E., Oturanc¸ G., Approximate solution of generalized pantograph equation by the differential transform method, Int.J.Nonlinear Sci. 8 (2007) 159-168.
  • Is¸ık O.R., G¨uney Z., Sezer M., Bernstein series solutions of pantograph equations using polynomial interpolation, J. Dif. Equ. Appl,. in press, (2010). DOI: 10.1080/10236198.2010.496456.
  • Oliveira F.A., Collacation and residual correction, Numer.Math. 36 (1980) 27-31.
  • C¸ elik ˙I., Collacation method and residual correction using Chebyshev series, Appl. Math. Comput. 174 (2006) 910-920.
  • Y¨uzbas¸ı S¸.,An efficient algorithm for solving multi-pantograph equation systems, Computers and Mathematics with Applications, in press (2012), doi:10.1016/j.camwa.2011.12.062.
  • Evans D. J., Raslan K. R., The Adomain decomposition method for solving delay differential equation, Int. J. Comput. Math. 82 (2005), 49–54.

Residual correction of the Hermite polynomial solutions of the generalized pantograph equations

Year 2015, Volume: 3 Issue: 2, 118 - 125, 19.01.2015

Şuayip Yüzbaşı Emrah Gök Mehmet Sezer

Abstract

References

  • Yusufo˘glu E., An efficient algorithm for solving generalized pantograph equations with linear functional argument, Appl. Math. Comput., 217 (2010) 3591-3595.
  • Sezer M., .Aky¨uz-Das¸cıo˘glu A, A Taylor method for numerical solution of generalized pantograph equations with lineer functional argument, J. Comput. Appl. Math., 200 (2007) 217-225.
  • Yu Z.-H., Variational iteration method for solving the multi-pantograph delay equation, Physics Letters A 372 (2008) 6475-6479.
  • Y¨uzbas¸ı S¸., S¸ahin N., Sezer M., A Bessel collocation method for numerical solution of generalized pantograph equations, Numer Methods Partial Differential Equations 28 (2012) 1105-1123.
  • Liu M.Z., Li D., Properties of analytic solution and numerical solution of multi-pantograph equation, Appl. Math. Comput. 155 (2004) 853-871.
  • Yalc¸ınbas¸ S., Aynig¨ul M., Sezer M., A collocation method using Hermite polynomials for approximate solution of pantograph equations, J. Frank. Inst. 348 (2011) 1128–1139.
  • Saadatmandi A., Dehghan M., Variational iteration method for solving a generalized pantograph equation, Comput. Math. Appl. 58(2009) 2190-2196.
  • Keskin Y., Kurnaz A., Kiris¸ M.E., Oturanc¸ G., Approximate solution of generalized pantograph equation by the differential transform method, Int.J.Nonlinear Sci. 8 (2007) 159-168.
  • Is¸ık O.R., G¨uney Z., Sezer M., Bernstein series solutions of pantograph equations using polynomial interpolation, J. Dif. Equ. Appl,. in press, (2010). DOI: 10.1080/10236198.2010.496456.
  • Oliveira F.A., Collacation and residual correction, Numer.Math. 36 (1980) 27-31.
  • C¸ elik ˙I., Collacation method and residual correction using Chebyshev series, Appl. Math. Comput. 174 (2006) 910-920.
  • Y¨uzbas¸ı S¸.,An efficient algorithm for solving multi-pantograph equation systems, Computers and Mathematics with Applications, in press (2012), doi:10.1016/j.camwa.2011.12.062.
  • Evans D. J., Raslan K. R., The Adomain decomposition method for solving delay differential equation, Int. J. Comput. Math. 82 (2005), 49–54.
There are 13 citations in total.

Details

Journal Section Articles
Authors

Şuayip Yüzbaşı This is me

Emrah Gök This is me

Mehmet Sezer This is me

Publication Date January 19, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Yüzbaşı, Ş., Gök, E., & Sezer, M. (2015). Residual correction of the Hermite polynomial solutions of the generalized pantograph equations. New Trends in Mathematical Sciences, 3(2), 118-125.
AMA Yüzbaşı Ş, Gök E, Sezer M. Residual correction of the Hermite polynomial solutions of the generalized pantograph equations. New Trends in Mathematical Sciences. January 2015;3(2):118-125.
Chicago Yüzbaşı, Şuayip, Emrah Gök, and Mehmet Sezer. “Residual Correction of the Hermite Polynomial Solutions of the Generalized Pantograph Equations”. New Trends in Mathematical Sciences 3, no. 2 (January 2015): 118-25.
EndNote Yüzbaşı Ş, Gök E, Sezer M (January 1, 2015) Residual correction of the Hermite polynomial solutions of the generalized pantograph equations. New Trends in Mathematical Sciences 3 2 118–125.
IEEE Ş. Yüzbaşı, E. Gök, and M. Sezer, “Residual correction of the Hermite polynomial solutions of the generalized pantograph equations”, New Trends in Mathematical Sciences, vol. 3, no. 2, pp. 118–125, 2015.
ISNAD Yüzbaşı, Şuayip et al. “Residual Correction of the Hermite Polynomial Solutions of the Generalized Pantograph Equations”. New Trends in Mathematical Sciences 3/2 (January 2015), 118-125.
JAMA Yüzbaşı Ş, Gök E, Sezer M. Residual correction of the Hermite polynomial solutions of the generalized pantograph equations. New Trends in Mathematical Sciences. 2015;3:118–125.
MLA Yüzbaşı, Şuayip et al. “Residual Correction of the Hermite Polynomial Solutions of the Generalized Pantograph Equations”. New Trends in Mathematical Sciences, vol. 3, no. 2, 2015, pp. 118-25.
Vancouver Yüzbaşı Ş, Gök E, Sezer M. Residual correction of the Hermite polynomial solutions of the generalized pantograph equations. New Trends in Mathematical Sciences. 2015;3(2):118-25.