A novel ninth-order root-finding algorithm for nonlinear equations with implementations in various software tools

Abstract

Nonlinear phenomena are prevalent in numerous fields, including economics, engineering, and natural sciences. Computational science continues to advance through the development of novel numerical schemes and the refinement of existing ones. Ideally, these numerical systems should offer both high-order convergence and computational efficiency. This article introduces a new three step algorithm for solving nonlinear scalar equations, aiming to meet these criteria. The proposed approach requires six function evaluations per iteration and achieves ninth-order convergence. To demonstrate the efficiency of the technique, various numerical examples are shown. Implementations of the method are available in both Maple and Python, and it can be readily adapted for use in other computational environments.

Keywords

Root-finding algorithm / Nonlinear equations / Implementations / Halley method / Exponential method

Funding

None.

Conflict of interest

The authors declare that they have no competing interests.

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