The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass |
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| Authors: | S.A. Yousefi |
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| Affiliation: | a Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iranb Faculty of Basic Sciences, Babol University of Technology, Babol, Mazandaran, Iranc Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran, Iran |
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| Abstract: | Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions. The properties of Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given parabolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique. |
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| Keywords: | One-dimensional parabolic equation Nonlocal boundary conditions Bernstein basis Operational matrices Specification of mass Integral condition |
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