Comparative Study Between Euler Arithmetic and Euler Cube Scheme for Solving Ordinary Differential Equation in Resistor-Inductor (RL) Circuit Equation

Abstract

Ordinary differential equations play a central role in modeling dynamic processes in electrical engineering and applied sciences. While Euler’s method remains widely used due to its simplicity, its numerical accuracy and stability are strongly affected by step size selection. This paper presents a comparative study of the Euler Arithmetic (EA) and Euler Cube (EC) schemes for solving firstorder ordinary differential equations arising from resistor–inductor (RL) circuit models. The Euler Cube scheme extends the classical Euler formulation through cubemean averaging, enabling improved numerical stability without increasing computational complexity. Numerical experiments conducted on multiple RLbased test equations demonstrate that the EC scheme yields lower absolute error than EA at moderate step sizes, while both approaches retain firstorder convergence. At sufficiently small step sizes, the two methods converge to comparable accuracy. The results indicate that Euler Cube is a robust alternative for engineering simulations where accuracy and computational efficiency must be balanced.