(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this study, bisection algorithm, golden ratio and Fibonacci search algorithms are used to find the roots of univariate, logarithmic, trigonometric, exponential and polynomial functions. The results obtained from these methods are compared, and the fundamental principles, advantages, and disadvantages of each algorithm are discussed in terms of numerical stability. The approximation to the root with minimal error and the fewest steps is analyzed. The study concludes with results and recommendations based on comparative analysis.