31Jan 2017

A NOVEL APPROACH FOR THE SOLUTION OF A CLASS OF URYSOHN INTEGRALE QUATIONS USING BERNSTEIN POLYNOMIALS.

  • Asst. Prof. Dr., Dept. Of Accounting by IT, Cihan University, Campus, Sulaimaniya, Kurdistan Iraq.
Crossref Cited-by Linking logo
  • Abstract
  • Keywords
  • References
  • Cite This Article as
  • Corresponding Author

In this paper a novel technique implementing Bernstein polynomials is introduced for the numerical solution of a classof Urysohn integral equations. These polynomials are utilized toreduce the solution of the given problem to the solution of a system of non-linear algebraic equations. The remaining set of nonlinear equations is solved numerically by using the approach to yield truncated Bernstein series coef?cients of the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.

  1. Eskandarughlu, H.E. Derili Gherjalar, H. Mohammadikia, A. Arzhang, Austra. J. Basic Appl. Sci.7 (1),
  2. 286–294 (2013).
  3. Singh, G. Nelakanti, J. Kumar, the Sci. World J. 2014, Article ID 150483 (2014).
  4. Maleknejad, K. Nedaiasl, J. Int. Equ. Appl. 25(3), 321–454 (2013); K.Maleknejad, K.Nedaiasl, B.Moradi,ProceedingsoftheWorldCongressonEngineering,2013, Vol I.
  5. Saberi-Nadja?, M. Heidari, Comput. Math.Applications 60, 2058–2065 (2010).
  6. Jafarian, Z. Esmailzadeh, L. Khoshbakhti, Appl. Math. Sci.7(28), 1375–1385 (2013).
  7. Awawdeh, A. Adawi, Int. Math. Forum17, 805–817 (2009).
  8. K. Golmankhaneh, N.A. Porghoveh, D. Baleanu, Rom. Rep. Phys. 65, 350–361 (2013);
  9. Rostamy, M. Alipour, H. Jafari, D. Baleanu, Rom. Rep. Phys. 65, 334–349 (2013);
  10. K. Golmankhaneh, Ali K. Golmankhaneh, D. Baleanu, Rom. Rep. Phys.63, 609–623 (2011);
  11. K. Golmankhaneh, Ali K. Golmankhaneh, D. Baleanu, Sig. Proce. 91(3), 446–451 (2011).
  12. Kadem, D. Baleanu, Rom. J. Phys. 56, 332–338 (2011);
  13. J. Yang, D. Baleanu, W.P. Zhong, Proc. Romanian Acad. A14, 127–133 (2013).
  14. M.O. Anwar, F. Jarad, D. Baleanu, F. Ayaz, Rom. J. Phys.58, 15–22 (2013); Jafarian et al., Rom. J. Phys.58, 694–702 (2013);
  15. J. Rosales Garcia, M.G. Calderon, J.M. Ortiz, D. Baleanu, Proc. Romanian Acad. A 14, 42–47 (2013).
  16. Jafarian, S. Measoomy Nia, J. Hyperstruct. 2(1), 53–71 (2013);Jafarian, S. Measoomy Nia, Appl. Math. Model. 37(7), 5027–5038 (2013); Jafarian, S. Measoomy Nia, Int. J. Math. Mod.Numer. Opt.n 4(3), 225–237 (2013);
  17. Jafarian, S. Measoomy Nia, A.K. Golmankhaneh, D. Baleanu, Adv. Diff. Equ. DOI:10.1186/1687-1847-2013-123.
  18. Effati, R. Buzhabadi, Neural Comput. Appl., DOI:10.1007/s00521-010-0489-y.
  19. E. Lagaris, A. Likas, D.I. Fotiadis, IEEE Transac. Neur. Netw. 9(5), 987–1000 (1998).
  20. Reinkenhof, Int. J. Numer. Methods Engrg. 11, 1627 (1986).
  21. Kreyszig, Int. J. Numer. Methods Engrg.14, 292 (1979).
  22. N. Mandal and S. Bhattacharya, Appl. Math.Comput. 190, 1707 (2007).
  23. I. Bhatti and P. Bracken, J. Comput.Appl.Math.205, 272 (2007).
  24. Muna M. Mustafa & Khawla A .AL-Zubaidy. Use of Bernstein Polynomial in Numerical Solution of Nonlinear Fred Holm Integral Equation. Eng. & Tech. Journal, Vol. 29, No. 1, 2011
 

[Jumah Aswad Zarnan. (2017); A NOVEL APPROACH FOR THE SOLUTION OF A CLASS OF URYSOHN INTEGRALE QUATIONS USING BERNSTEIN POLYNOMIALS. Int. J. of Adv. Res. 5 (Jan). 2156-2162] (ISSN 2320-5407). www.journalijar.com

Jumah Aswad Zarnan
Asst. Prof. Dr., Dept. Of Accounting by IT, Cihan University \ Campus \ Sulaimaniya, Kurdistan Iraq

DOI:

Article DOI: 10.21474/IJAR01/2990      
DOI URL: http://dx.doi.org/10.21474/IJAR01/2990

Download Full Paper

Download PDF No. of Downloads: 10 | No. of Views: 88