Abstract
In this paper the hybrid block-pulse function and Bernstein polynomials are introduced to approximate the solution of linear Volterra integral equations. Both second and first kind integral equations, with regular, as well as weakly singular kernels, have been considered. Numerical examples are given to demonstrate the applicability of the proposed method. The obtained results show that the hybrid block-pulse function and Bernstein polynomials are more accurate that Bernstein polynomials. AMS Subject Classification: 65Rxx, 45Exx, 45D05
Highlights
Bernstein polynomials (BP) have been recently used for the solution of some nonlinear integro-differential equations, both BVP, by Yuzbasi [1] and Islam & Hossain [2]
There are some applications of Bernstein polynomials, for example see [10], and extend them for hybrid Bernstein polynomials and block-pulse functions
In this paper we have developed a simple method, based on approximation of the unknown function on the hybrid block-pulse function and Bernstein polynomials basis, for the solution of Volterra integral equations with regular kernels, as well as weakly singular kernels, that is Abels integral equation
Summary
Bernstein polynomials (BP) have been recently used for the solution of some nonlinear integro-differential equations, both BVP, by Yuzbasi [1] and Islam & Hossain [2]. These have been used to solve some classes of mathematical equations by [3, 4, 5, 6, 7, 8]. In this paper we have developed a simple method, based on approximation of the unknown function on the hybrid block-pulse function and Bernstein polynomials basis, for the solution of Volterra integral equations with regular kernels, as well as weakly singular kernels, that is Abels integral equation. The present method avoids any such computational difficulty, and uses a very direct algorithm for computation of the unknown function
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