Finding Approximate Roots of Nonlinear Equations by Using New Sixth-Order Convergence

Document Type : Original Article

Authors
Rzgar Fariq Mahmood 1
Mediya B. Mrakhan 2
Omed Q. Ahmed 3
1 Department of Mathematics, College of Education, University of Garmian, Kalar, Sulaymaniyah, Iraq
2 Department of Chemistry, College of Science, University of Garmian, Kalar, Sulaimanyah, Iraq.
3 Department of Mathematics, College of Education, University of Garmian, Kalar, Sulaimanyah, Iraq.
10.24271/psr.2022.161694
Abstract
In this study, we introduced new iterative techniques, for the purpose solving nonlinear equations. The new approaches are based on the auxiliary equation and Newton's method, respectively. Our method's a convergence analysis is explained. The novel approach is found to have convergence order of six. Numerical experiments show that the new method work better than well-known iterative methods and is similar to them.
Keywords
Newton’s Raphson
Iterative Methods
Auxiliary Equation
Order of Convergence
Crossmark
Subjects
Passer Journal of Basic and Applied Sciences
Volume 4, Special issue
This special issue is related to the 9th Scientific Conference of University of Garmian: Pure Sciences and Technology Applications (SCUG-PSTA-2022) October 26–27, 2022. (All the manuscripts have been peer-reviewed.)
November 2022
Pages 179-186