Convergence analysis of Picard-Abbas hybrid iterative process

Abstract

Iterative methods play a crucial role in numerical analysis and optimization problems. This paper introduces a hybrid fixed-point iterative process and compares its convergence rate with the established Abbas iterative approach, using Berinde’s criteria. Additionally, the stability and data dependency of the improved iterative process are established. This study’s purpose is to demonstrate the superiority, in terms of convergence speed, of the hybrid approach and provide further insights into its stability and data dependency. Furthermore, we apply the iterative process to find solutions of delay differential equations.