Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications

Mudassir Shams, Nasreen Kausar () and Ioana Alexandra Șomîtcă ()
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Mudassir Shams: Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Nasreen Kausar: Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul 34220, Türkiye
Ioana Alexandra Șomîtcă: Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Baritiu Street, no 26–28, 40027 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 22, 1-26

Abstract: It is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introduced. Based on theoretical research, a novel family of simple root-finding schemes based on multiplicative calculus has been devised, with a convergence order of seven. The symmetry in the pie graph of the convergence–divergence areas demonstrates that the method is stable and consistent when dealing with nonlinear engineering problems. An extensive examination of the numerical results of the engineering applications is presented in order to assess the effectiveness, stability, and consistency of the recently established method in comparison to current methods. The analysis includes the total number of functions and derivative evaluations per iteration, elapsed time, residual errors, local computational order of convergence, and error graphs, which demonstrate our method’s better convergence behavior when compared to other approaches.

Keywords: nonlinear equations; multiplicative calculus; iterative-scheme; pie chart; percentage convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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