Derivative Free Fourth Order Solvers of Equations with Applications in Applied Disciplines

Symmetry

IoannisK. Argyros¹  FouadOthman Mallawi²  Ramandeep Behl²  J.A. Tenreiro Machado³ 

[1] Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA;Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;ISEP-Institute of Engineering, Polytechnic of Porto Department of Electrical Engineering, 431 4294-015 Porto, Portugal;

关键词: divided difference;    radius of convergence;    Kung–Traub method;    local convergence;    Lipschitz constant;    Banach space;   

DOI  :  10.3390/sym11040586

来源: DOAJ

【 摘 要 】

This paper develops efficient equation solvers for real- and complex-valued functions. An earlier study by Lee and Kim, used the Taylor-type expansions and hypotheses on higher than first order derivatives, but no derivatives appeared in the suggested method. However, we have many cases where the calculations of the fourth derivative are expensive, or the result is unbounded, or even does not exist. We only use the first order derivative of function $\Omega$ in the proposed convergence analysis. Hence, we expand the utilization of the earlier scheme, and we study the computable radii of convergence and error bounds based on the Lipschitz constants. Furthermore, the range of starting points is also explored to know how close the initial guess should be considered for assuring convergence. Several numerical examples where earlier studies cannot be applied illustrate the new technique.

【 授权许可】

Unknown