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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

A Computational Method Based on Bernstein Polynomials for Solving FredholmIntegro-Differential Equations under Mixed Conditions

Miloud Moussai1 and Lakhdar Chiter2
  • 1 University of M’sila, Algeria
  • 2 University of Setif, Algeria

Abstract

In this study, a computational method for solving linear FredholmIntegro-Differential Equation (FIDE) of the first order under the mixed conditions using the Bernstein polynomials. First, we present some properties of these polynomials and the method is explained. These properties are then used to convert the integro-differential equation to a system of linear algebraic equations with unknown Bernstein coefficients. Using Galerkin method, we give an approximate solution. This method seems very attractive and simple to use. Illustrative examples show the efficiency and validity of the method we discuss the results using error analysis, the results are discussed.

Journal of Mathematics and Statistics
Volume 13 No. 1, 2017, 30-37

DOI: https://doi.org/10.3844/jmssp.2017.30.37

Submitted On: 21 October 2016 Published On: 27 February 2017

How to Cite: Moussai, M. & Chiter, L. (2017). A Computational Method Based on Bernstein Polynomials for Solving FredholmIntegro-Differential Equations under Mixed Conditions. Journal of Mathematics and Statistics, 13(1), 30-37. https://doi.org/10.3844/jmssp.2017.30.37

Open AccessCopyright: © 2017 Miloud Moussai and Lakhdar Chiter. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Bernstein Polynomials
  • Linear FredholmIntegro-Differential Equations of the First Order
  • Mixed Conditions
  • Galerkin Method
  • Numerical Analysis
  • Error Estimates