Solving nonlinear boundary value problems by the Galerkin
method with sinc functions

• Authors: Sertan Alkan , Aydin Secer
• Languages of publication: EN

Abstracts

EN

In this paper, the sinc-Galerkin method is used
for numerically solving a class of nonlinear differential
equations with boundary conditions. The importance of
this study is that sinc approximation of the nonlinear term
is stated as a new theorem. The method introduced here is
tested on some nonlinear problems and is shown to be a
very efficient and powerful tool for obtaining approximate
solutions of nonlinear ordinary differential equations.

Keywords

EN

nonlinearity; sinc-Galerkin method; boundaryvalue problems

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

received

14 - 11 - 2015

accepted

26 - 11 - 2015

online

31 - 12 - 2015

Contributors

author

Sertan Alkan

• Department of Mathematics,
  Mustafa Kemal University, Hatay, Turkey

author

Aydin Secer

• Department of Mathematical Engineering, Yildiz Technical
  University, Istanbul, Turkey

References

• [1] J. He, Commun. Nonlinear Sci. Numer. Simul. 2, 230 (1997)[Crossref]
• [2] J.H. He, Comput. Method. Appl. M. 167, 69 (1998)
• [3] Z.M. Odibat, O. Momani, Int. J. Nonlinear Scie. Numer. Simul. 7,27 (2006)
• [4] S. Liao, Y. Tan, Stud. Appl. Math. 119, 297 (2007)
• [5] S. Liao, Appl. Math. Comput. 147, 499 (2004)
• [6] S. Abbasbandy,Phys. Lett. A, 360, 109 (2006)
• [7] H. Jafari, S. Seifi, Commun. Nonlinear Sci. Numer. Simul. 14,2006 (2009)[Crossref]
• [8] N.T. Shawagfeh, Appl. Math. Comput. 131, 517 (2002)
• [9] E. Babolian, J. Biazar, Appl. Math. Comput. 132, 167 (2002)
• [10] J.L. Li, J. Comput. Appl. Math., 228, 168 (2009)
• [11] C. Chun, H. Jafari, Y.I. Kim, Comput. Math. Appl. 57, 1226 (2009)
• [12] D.D. Ganji, Phys. Lett. A 355, 337 (2006)
• [13] U. Lepik, Appl. Math. Comput. 185, 695 (2007)
• [14] G. Hariharan, K. Kannan, K.R. Sharma, Appl.Math. Comput. 211,284 (2009)
• [15] L. Yuanlu, Commun. Nonlinear Sci. Numer. Simul. 15, 2284(2010)[Crossref]
• [16] S.A. Yousefi, Appl. Math. Comput. 181, 1417 (2006)
• [17] S.G. Venkatesh, S.K. Ayyaswamy, S.R. Balachandar, Comput.Math. Appl. 63, 1287 (2012)
• [18] F. Stenger, J. Approx. Theory 17, 222 (1976)[Crossref]
• [19] F. Stenger, Math. Comp. 33, 85 (1979)
• [20] J. Rashidinia, N. Nabati, Comput. Appl. Math. 32, 315 (2013)
• [21] M. El-Gamel, A.I. Zayed, Comput. Math. Appl. 48, 1285 (2004)
• [22] M. Zarebnia, M. Sajjadian,Math. Comput. Model. 56, 218 (2012)
• [23] A. Secer, S. Alkan, M.A. Akinlar, M. Bayram, Bound. Value Probl.2013, 281 (2013)[Crossref]
• [24] S. Alkan, A. Secer, Math. Probl. Eng. 2015, 217348 (2015)
• [25] A. Secer, M. Kurulay, M. Bayram, M.A. Akinlar, Bound. ValueProbl. 2012, 1 (2012)
• [26] S. Alkan, NTMSci 2, 01 (2014)
• [27] J. Lund, K.L. Bowers, Sinc methods for quadrature and differentialequations, SIAM, Philadelphia (1992)
• [28] F. Stenger, Handbook of Sinc numerical methods, CRC Press,USA (2010)

Identifiers

DOI

10.1515/phys-2015-0050