Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration

Abstract

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems.

Keywords

• fixed point
• nonlinear volterra integral equations
• picard's three step iteration
• convergence
• data dependency