Numerical Solution of Ordinary Differential Equations with Error Analysis

Mathematics — 2025, Undergraduate

This study examined numerical methods for the solution of ordinary differential equations and their associated errors. Euler, improved Euler, and Runge-Kutta style methods were applied to representative initial-value problems, and accuracy was assessed against exact solutions. The findings revealed that higher-order methods achieved greater accuracy at comparable step sizes, while error grew predictably with step size. The study observed stability limitations for stiff problems. It recommends combined use of order and step-size control in practice.

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