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Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi

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  • Ali Özyapıcı
  • Zehra B. Sensoy
  • Tolgay Karanfiller

Abstract

In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.

Suggested Citation

  • Ali Özyapıcı & Zehra B. Sensoy & Tolgay Karanfiller, 2016. "Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, October.
    • Handle: RePEc:hin:jjmath:8174610
    DOI: 10.1155/2016/8174610
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    1. James Englehardt & Jeff Swartout & Chad Loewenstine, 2009. "A New Theoretical Discrete Growth Distribution with Verification for Microbial Counts in Water," Risk Analysis, John Wiley & Sons, vol. 29(6), pages 841-856, June.
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    Cited by:

    1. Mudassir Shams & Nasreen Kausar & Ioana Alexandra Șomîtcă, 2024. "Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications," Mathematics, MDPI, vol. 12(22), pages 1-26, November.

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