Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials

Volume 11, Issue 5, pp 624--634 http://dx.doi.org/10.22436/jnsa.011.05.04
Publication Date: March 29, 2018 Submission Date: March 21, 2017 Revision Date: November 18, 2017 Accteptance Date: March 01, 2018

Authors

Abdelkrim Bencheikh - Department of Mathematics, University of Ouargla, 30000 Ouargla, Algeria. Lakhdar Chiter - Department of Mathematics, University of Setif 1, 19000 Setif, Algeria. Tongxing Li - LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China. - School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China.


Abstract

Some problems from modern physics and science can be described in terms of partial differential equations with nonlocal conditions. In this paper, a numerical method which employs the orthonormal Bernstein polynomials basis is implemented to give the approximate solution of integro-differential parabolic equation with purely nonlocal integral conditions. The properties of orthonormal Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given integro-differential parabolic equation to the solution of algebraic equations. An illustrative example is given to demonstrate the validity and applicability of the new technique.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Abdelkrim Bencheikh, Lakhdar Chiter, Tongxing Li, Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 624--634

AMA Style

Bencheikh Abdelkrim, Chiter Lakhdar, Li Tongxing, Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials. J. Nonlinear Sci. Appl. (2018); 11(5):624--634

Chicago/Turabian Style

Bencheikh, Abdelkrim, Chiter, Lakhdar, Li, Tongxing. "Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 624--634


Keywords


MSC


References