Abstract
This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed family is derived by implementing approximation through a straight line. The presence of an arbitrary parameter in the proposed family improves convergence characteristic of the simple fixed point iteration as it has a wider domain of convergence. Furthermore, we propose many two-step predictor–corrector iterative schemes for finding fixed points, which inherit the advantages of the proposed fixed point iterative schemes. Finally, several examples are given to further illustrate their efficiency.
Highlights
The fixed point iteration is probably the simplest and most important root-finding algorithm in numerical analysis [1,2]
We can obtained the following fixed point iterative method based on expression (18)
We developed a one-parameter class of fixed point iteration methods for generating a sequence approximating fixed points of nonlinear equations
Summary
Vinay Kanwar 1 , Puneet Sharma 1,2 , Ioannis K.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
