Improved bracketing parabolic method for numerical solution of nonlinear equations

Vladimir Kodnyanko

Applied Mathematics and Computation, 2021, vol. 400, issue C

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.

Keywords: Nonlinear equation; Bisection method; Müller method; Brent method; Ridders method; Parabolic method; Improved parabolic method; Speed method (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000436

DOI: 10.1016/j.amc.2021.125995

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