An Effective Root-Finding Toolbox Using Computational Argumentation

This paper introduces a novel knowledge management system built on the Raison platform, which leverages computational argumentation technology, to determine the optimal root-finding solver based on user-selected attributes of the solver, the function, and root multiplicity. The goal is to automate the selection process for solving nonlinear equations while offering a tool that is both educationally valuable for university-level instruction and practically useful for researchers. The system evaluates solvers implemented using MATLAB programs, including Bisection, fzero (based on Brent-Dekker’s method), ITP for bracket methods, and Secant, Newton, and Muller for open methods. It also utilizes MATLAB’s roots and solver functions. To validate the methodology, several scenarios were developed, including a real-life problem in electrical circuits which is included in this paper, and the system’s decisions were compared with those of ChatGPT, Gemini, and the numerical results of these methods. This analysis highlights the system’s ability to align with expert reasoning and provide human-readable explanations.