Balancing Precision and Efficiency: Comparative Analysis of Numerical Methods for Initial Value Problems
Year: 2025
Type: article
Abstract: In this study, the performance of four numerical techniques for solving Initial Value Problems (IVPs) in ordinary differential equations: Euler's method, Runge-Kutta fourthorder (RK4), Heun's method, and Milne's method is evaluated.Based on the analysis, RK4 and Milne's methods provide excellent accuracy and sustain low absolute errors over time, thus making them perfect for high-precision tasks.Heun's method offers a balance between accuracy and efficiency, making it a moderate advance over Euler's.On the other hand, Euler's method exhibits the biggest absolute errors, particularly when step sizes are bigger, which makes it less appropriate for applications that demand a high level of precision.The findings show that while choosing a numerical approach for IVPs, accuracy and computational efficiency must be balanced.
Authors: Ndipmong A. Udoh, Udechukwu P. Egbuhuzor
Institution: Federal University Otuoke
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411354035