Multipurpose modified iterative solver for nonlinear equations

  • Saher Afshan Department of Mathematics and Statistics, Institute of Business Management
  • Abdul Hanan Sheikh Department of Mathematics and Statistics, Institute of Business Management
  • Fatima Riaz Department of Mathematics and Statistics, Institute of Business Management
  • Rahim Bux Khokhar Department of BS & RS, Mehran University of Engineering and Technology

Abstract

Non-linear Eq.s occur as a sub-problem in a wide variety of engineering and scientific domains. To deal with the complexity of Non-linear Eq.s, it is often required to use numerical procedures, which are the most suitable method to employ in certain circumstances. Many classic iterative approaches have been regularly employed for various situations; nevertheless, the convergence rate of those methods is low. In many cases, an iterative approach with a faster convergence rate is needed. This is something that classical methods like the Newton-Raphson Method (NRM) cannot provide. As part of this investigation, a modification to the NRM has been suggested to speed up convergence rates and reduce computational time. Ultimately, this research aims to improve the NRM, resulting in a Modified Iterative Method (MIM). The proposed method was thoroughly examined. According to the research, the convergence rate is higher than that of NRM. The proposed method delivers more accurate results while reducing computational time and requiring fewer iterations than earlier methods. The numerical findings confirm that the promised performance is correct. The results include the number of iterations, residuals, and computing time. This innovative technique, which is appropriate to any Non-linear equation, produces more accurate approximations with less iteration than conventional methods, and it is appropriate to any Non-linear equation.

Published
Jul 21, 2023
How to Cite
AFSHAN, Saher et al. Multipurpose modified iterative solver for nonlinear equations. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 42, n. 3, p. 167-176, july 2023. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/2556>. Date accessed: 24 may 2024. doi: http://dx.doi.org/10.22581/muet1982.2303.17.
Section
Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License