Enhancing Simulation Accuracy in Radioactive Decay Models: Comparative Analysis of Euler and RK2 Methods for Interactive Systems

The modeling of radioactive decay processes has long been essential in fields such as nuclear physics, embedded systems, and educational simulations. Traditionally, the Euler method has been used to numerically solve the differential equations governing these phenomena. However, Euler’s method exhibits significant limitations in terms of accuracyAccuracy and stability, particularly in coupled systems or stiff mathematical configurations. To address this issue, this study presents a detailed comparison between the Euler method and the second-order Runge-Kutta method (RK2), aiming to evaluate their performance in terms of error accumulation, temporal fidelity, and the ability to preserve system dynamics. The goal is to determine which method is more suitable for simulations that demand high precision and computational efficiency. Numerical simulations were conducted for dual decay, cyclic decay, and thermistor cooling models using normalized time steps (Δt = 0.01 and 0.05). The results were compared against analytical solutions and analyzed through logarithmic error plots. RK2 consistently outperformed the Euler method, reducing absolute error by up to 80%. For instance, in the dual decay model, Euler’s error reached 3.41 units, while RK2 kept it below 0.62. Moreover, RK2 preserved the oscillatory dynamics in cyclic models and accurately predicted thermal thresholds in thermistor simulations. RK2 proves to be significantly more suitable for dynamic simulations where numerical precision and stability are critical. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.