A NOVEL FIXED POINT ITERATION PROCESS APPLIED IN SOLVING DELAY DIFFERENTIAL EQUATIONS

A NOVEL FIXED POINT ITERATION PROCESS APPLIED IN SOLVING

Abstract

In this paper we introduce a new four-step iteration process, called the Picard-Noor hybrid iterative process, and prove that this new iteration scheme converges to the unique fixed point of contraction operators. We then show that it converges faster than all of Picard, Mann, Noor, Krasnoselskii, Ishiwaka, Picard-Mann, Picard-Krosnoselskii, and Picard-Ishiwaka iteration processes with numerical examples visualized in graphs and tables to substantiate our claims. Data dependence result is proved and stability of the new process is shown. Our result is applied to the approximation of the solution of delay differential equations. Our results generalize and extend other results in literature.