Numerical solution of Generalized Abel s integral equations using Bernoulli collocation method

In this paper, an approximate method for solving the Generalized Abel s integral equations is proposed. The method is based on expanding the unknown function in terms of Bernoulli polynomials. Then, the collocation method is applied to reduce the solution of the Generalized Abel s integral equation to the one of solving a system of algebraic equations. Results of numerical examples are presented, which illustrate that the proposed method achieve good accuracy even using a small number of Bernoulli polynomials.