A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials

Subject Areas : International Journal of Industrial Mathematics

M.  Mohamadi ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
E.  Babolian ² (Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
S.  Yousefi ³ (Department of Mathematics, Shahid Beheshti University, G. C. Tehran, Iran.)

Received: 2017-03-03 Accepted : 2017-10-22 Published : 2018-01-01

Keywords: Transformation matrices, Volterra integral equation, Bernstein polynomials, Operational matrices,

Abstract :

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.