BERNOULLI SERIES SOLUTIONS FOR LINEAR INTEGRAL EQUATIONS
MOSTEFA NADIR *
Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, Algeria.
*Author to whom correspondence should be addressed.
The goal of this work is to calculate the approximate solution of linear integral equations using truncation Bernoulli series approximation. After substituting the Bernoulli expansions for the given functions of the equation and the unknown one, we apply the collocation method in order to reduce the equation to a linear system, the solution of this latter gives the Bernoulli coefficients and consequently the solution of the equation. The convergence and the error analysis of this method are studied and compared with the ones of other papers.
Keywords: linear integral equations;, Bernoulli polynomials;, collocation methods.