A new family of twentieth order convergent methods with applications to nonlinear systems in engineering

  • Hameer Akhtar Abro Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro Pakistan
  • Muhammad Mujtaba Shaikh Supply Chain and Operations Management Research Group, Mehran University of Engineering and Technology, Jamshoro, Pakistan

Abstract

A new family of iterative methods with a strong converging order of twenty to solve nonlinear equations and systems is presented in this study. A simple strategy of blending some existing methods is used to develop the proposed family. The theoretical order of convergence is derived by employing Taylor’s series. The performance of the iterative methods in the proposed family is examined by applying the methods on real-world engineering problems. A nonlinear equation modeled by NASA for launching “Wind” satellite and some other complex applied systems, such as combustion problem, tank-reactor problem, kinematic synthesis mechanism, neurophysiology application and one boundary-value problem, have been solved to check the performance of the proposed family against other methods under similar test conditions. All the numerical results show that the proposed family converges very fast in complex and difficult problems as compared to other well-known methods. The methods in the proposed family have an efficiency improvement of 11.99% over the classical Newton method for scalar nonlinear equations.

Published
Jan 1, 2023
How to Cite
ABRO, Hameer Akhtar; SHAIKH, Muhammad Mujtaba. A new family of twentieth order convergent methods with applications to nonlinear systems in engineering. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 42, n. 1, p. 165-176, jan. 2023. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/1277>. Date accessed: 06 feb. 2023. doi: http://dx.doi.org/10.22581/muet1982.2301.15.
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License