Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials
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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
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
- Integro-differential parabolic equation
- purely nonlocal integral conditions
- orthonormal Bernstein polynomials
- operational matrix
MSC
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