Performance Evaluation of Root-Finding Methods for Nonlinear Equations

Mathematics — 2025, Undergraduate

This study evaluated the performance of root-finding methods for nonlinear equations. Bisection, regula falsi, secant, and Newton-type methods were implemented for representative equations, and convergence speed, accuracy, and robustness were compared. The findings revealed that derivative-based methods converged fastest for smooth roots, while bracket methods remained robust where derivatives were problematic. The study observed trade-offs between speed and reliability. It recommends method selection informed by function behaviour and starting conditions.

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