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Improved bracketing parabolic method for numerical solution of nonlinear equations

Author

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  • Kodnyanko, Vladimir

Abstract

An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.

Suggested Citation

  • Kodnyanko, Vladimir, 2021. "Improved bracketing parabolic method for numerical solution of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000436
    DOI: 10.1016/j.amc.2021.125995
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    Cited by:

    1. Fernández-Díaz, Julio M. & Menéndez-Pérez, César O., 2023. "A common framework for modified Regula Falsi methods and new methods of this kind," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 678-696.
    2. Bawar Mohammed Faraj & Shnyar Karim Rahman & Deni Adnan Mohammed & Bahadin Muhammad Hussein & Berivan Azad Salam & Khadija Rzgar Mohammed, 2022. "An Improved Bracketing Method For Numerical Solution Of Nonlinear Equations Based On Ridders Method," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 6(2), pages 30-33, September.

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