Abstract

This project focuses on three numerical methods — Bisection, Newton–Raphson, and Secant — to find the root of a nonlinear equation.
These methods are used when equations cannot be solved exactly and an approximate solution is needed.

Each method was implemented using GNU Octave to observe how fast and accurately it converges to the correct root.
Through repeated iterations, the methods improve an initial guess until the result becomes very close to the true value.

The comparison shows that all three methods reached the same solution (x = 2), but the Newton–Raphson method converged the fastest.
The study demonstrates how numerical methods are important in solving practical problems in mathematics, engineering, and computer science where analytical solutions are difficult or impossible to obtain.