Bernstein Polynomials for Solving Abels Integral Equation

Volume 3, Issue 4, pp 403--412 http://dx.doi.org/10.22436/jmcs.03.04.06

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Authors

Mohsen Alipour - Member of young research club, Islamic Azad University, Sari branch, P. O. Box 48164-194, Sari, Iran Davood Rostamy - Department of Mathematics, Imam Khomeini International University, P. O. Box 34149-16818, Qazvin, Iran

Abstract

This paper presents a numerical method for solving Abel’s integral equation as singular Volterra integral equations. In the proposed method, the functions in Abel’s integral equation are approximated based on Bernstein polynomials (BPs) and therefore, the solving of Abel’s integral equation is reduced to the solving of linear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Keywords

• Abel’s integral equations
• Singular Volterra integral equations
• Bernstein polynomials.

MSC

•  65R20
•  45E10
•  45D05

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