On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

Advances in Difference Equations

Mudassir Shams¹  Nazir Ahmad Mir²  Praveen Agarwal³  Nasreen Kausar⁴  Naila Rafiq⁵  Choonkil Park⁶ 

[1] Department of Mathematics and Statistics, Riphah International University I-14, 44000, Islamabad, Pakistan;Department of Mathematics and Statistics, Riphah International University I-14, 44000, Islamabad, Pakistan;Department of Mathematics, NUML, Islamabad, Pakistan;Department of Mathematics, Anand International College of Engineering, 303012, Jaipur, Rajasthan, India;Department of Mathematics, Harish-Chandra Research Institute, 211019, Allahabad, India;International Center for Basic and Applied Sciences, 302029, Jaipur, India;Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler, 34210, Istanbul, Turkey;Department of Mathematics, NUML, Islamabad, Pakistan;Department of Mathematics, Research Institute of Natural Science, Hanyang University, Seoul, South Korea;

关键词: Single and all roots;    Nonlinear system of equations;    Iterative methods;    Simultaneous methods;    Basins of attraction;    Boundary value problems;   

DOI  :  10.1186/s13662-021-03636-x

来源: Springer

【 摘 要 】

In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.

【 授权许可】

CC BY