Published October 21, 2026 | Version v1
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Numerical Integration in Physics Simulations: A Comparative Analysis of Euler, Semi-Implicit Euler, Verlet, and Trapezoidal Methods

Description

This paper presents a comparative analysis of four numerical integration methods—Explicit Euler, Semi-Implicit Euler, Verlet, and Trapezoidal Euler—within the context of physics simulations. By implementing a custom physics engine in Java, this study evaluates the stability, energy conservation, and computational performance of each method across standard benchmark scenarios, including free fall, spring-mass oscillation, and two-body spring systems. The findings demonstrate that Explicit Euler is unsuitable for oscillatory systems due to significant energy drift, whereas Semi-Implicit Euler markedly improves stability for smooth motion but fails during collision handling. Verlet integration exhibits near-perfect energy conservation across all test scenarios, and Trapezoidal Euler offers an effective balance between accuracy and computational cost. 

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Additional details

Software

Repository URL
https://github.com/Victor-Mielnik/Numerical-Integtaion-Physics-2D-INTERACTIVE
Programming language
Java
Development Status
Active

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