Picard-type iterations for solving Fredholm integral equations

Abstract

The theoretical solution of Fredholm integral equations involves the calculus of the inverse of an operator. However, for practical purposes, the calculus of this inverse could be not possible or very complicated. For this reason, our aim in this talk is to use iterative methods for approaching such inverse and therefore the solution of the given integral equation. In fact, we use Newton’s method to obtain a method with quadratic convergence. In addition, we also use Chebyshev’s method to obtain a method with cubic convergence. Next, we extend this idea to iterative methods with a given order of convergence. Finally, we propose the construction of Picard-type iterative methods that do not use derivatives or inverse operators.