Bernstein Operational Matrix Approach for Integro-Differential Equation Arising in Control theory
The aim of this paper is to propose an efficient numerical method for solving the integro-differential equations arising in many braches of sciences using Bernstein polynomials. This algorithm based on Bernstein polynomials approximation for integro-differential equations. First, Bernste...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
De Gruyter
2014-06-01
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Series: | Nonlinear Engineering |
Subjects: | |
Online Access: | https://doi.org/10.1515/nleng-2013-0024 |
Summary: | The aim of this paper is to propose an efficient
numerical method for solving the integro-differential
equations arising in many braches of sciences using Bernstein
polynomials. This algorithm based on Bernstein
polynomials approximation for integro-differential equations.
First, Bernstein operational matrix of differentiation
is derived using Bernstein polynomials and then applied
to solve integro-differential equations. The solutions obtained
by proposed method indicate that the approach is
easy to implement and computationally very attractive. A
good agreement between the obtained solution and some
well-known results has been obtained. Two numerical examples
are provided to show the advantage of using Bernstein
operational matrix. This method is capable of greatly
reducing the size of calculations while still maintaining
high accuracy of the numerical solution. |
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ISSN: | 2192-8029 |