Iterative estimate of the solution of nonlinear integral equations by picard’s method

Abstract

The paper considered the application of Picard’s iteration scheme in the approximation of solutions of operator equations in Banach spaces. Using Lipschitz continuity condition and the prescribed auxiliary scalar function, the location of existence of solution for a nonlinear integral equation of Fredholm type and second kind was obtained. The error estimate provided in the analysis was used to predict the convergence speed of the Picard’s iterates.

Keywords: Fredholm equations, Picard’s method, Lipschitz continuity condition, Fretchet derivative