Solution of Delay Differential Equation via N^v_1 Iteration Algorithm

Abstract

The aim of this paper is to define a  new iteration scheme $N^v_1$ which converges to a fixed point faster than some previously existing methods such as Picard, Mann, Ishikawa, Noor, SP, CR, S, Picard-S, Garodia, $K$ and $K^*$ methods etc. The effectiveness and efficiency of our algorithm is confirmed by numerical example and some strong convergence, weak convergence, $T$-stability and data dependence results for contraction mapping are also proven. Moreover, it is shown that differential equation with retarted argument is solved using $N^v_1$ iteration process.