Solving Ordinary Differential Equations Numerically: A Comparative Study of Euler, RK2, and RK4 Methods

This technical report presents a comparative study of three numerical methods for solving ordinary differential equations: Euler, RK2, and RK4. All methods were implemented from scratch in Python at step size h=0.1 over the interval [0,5]. RK4 achieves a maximum error of approximately 1.0 x 10^-6 compared to 0.0192 for Euler — roughly 19,000 times more accurate at the same step size. Source code available at: https://github.com/Mohamed10osama/numerical-ode-solver