A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics

Abstract

This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton’s method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.

Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations

“…To improve the efficiency of the one-step iterative schemes, a lot of iterative schemes based on two-step and three-step methods were depicted in [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], and some were based on the multi-composition of the functions [37][38][39][40].…”

An Efficient Twelfth-Order Iterative Method to Solve Nonlinear Equations with Applications

“…Application 1 (Blood Rheology Model, [7]). The study of blood's structure and flow characteristics is known as blood rheology.…”

“…Application 2 (Law of Blood Flow, [7]). This law was proposed in 1840 by French physician Jean Louis-Marie Poiseuille.…”

“…Application 3 (Fluid Permeability in Biogels, [7]). The following nonlinear model can be used to define the relationship between the hydraulic permeability and the pressure gradient to fluid velocity in the extracellular fibre matrix:…”

Design and Dynamical behavior of a fourth order family of iterative methods for solving nonlinear equations

“…There are problems in Engineering, Technology and in different fields of Science that require the solution of nonlinear equations. For example, Qureshi et al in [25] proposed a hybrid three-step iterative method for solving nonlinear equations in the field of medical science (blood rheology, population growth and neurophysiology). Also, Chand et al in [8] applied weight functions on several methods: Potra-Pták, two iterative schemes (optimal and non-optimal, respectively) of fourth and sixth orders of convergence and a family of optimal eighth order methods, aiming to solve problems related to the effect of water flow and other factors in the flow of open channels (rivers or canals) and the determination of fluid flow through tubes and pipes [7].…”