On Bernstein Polynomials Method to the System of Abel Integral Equations

Abstract EN

This paper deals with a new implementation of the Bernstein polynomialsmethod to the numerical solution of a special kind of singularsystem.

For this aim, first the truncated Bernstein series polynomialsof the solution functions are substituted in the given problem.

Usingsome properties of these polynomials, the solution of the problem isreduced to solve a linear system of algebraic equations.

In order to confirmthe reliability and accuracy of the proposed method, some weaklyAbel integral equations systems with comparisons are solved in detailas numerical examples.