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

Bencheikh, Abdelkrim ¹ ; Chiter, Lakhdar ² ; Li, Tongxing ³

¹ Department of Mathematics, University of Ouargla, 30000 Ouargla, Algeria
² Department of Mathematics, University of Setif 1, 19000 Setif, Algeria
³ 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

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 624-634.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.05.04

Classification : 33C45, 35K20, 42C05
Keywords: Integro-differential parabolic equation, purely nonlocal integral conditions, orthonormal Bernstein polynomials, operational matrix

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