A new iterative scheme for solving delay differential equation and oxygen diffusion problems

Abstract

The purpose of this paper is to introduce a new five steps iterative algorithm for approximating the solution of a delay differential equation and an oxygen diffusion problem. In addition, using our proposed iteration process, we state and prove some convergence results for approximating the fixed points of generalized (α,β)-nonexpansive type I mapping. In addition, we show that our proposed iterative scheme converges faster than some existing iterative schemes in the literature, data dependency, and stability results for our proposed iterative scheme are established with an analytical and numerical example given to justify our claim. Lastly, we established that the D-iterative scheme introduced by [8] and the AG-iterative scheme introduced by [21] have the same rate of convergence.