Comparison of the Euler Method, Fourth-Order Runge-Kutta Method, and Runge-Kutta-Fehlberg Method in Solving an RLC System

Abstract

This article discusses a comparison of numerical methods in solving systems of differential equations in resistor-inductor-capacitor (RLC) circuits. The methods used include the Euler method, the fourth-order Runge-Kutta (RK4), and the Runge-Kutta-Fehlberg (RKF). The circuit model is expressed in the form of a second-order differential equation system which is then transformed into a first-order system to facilitate numerical solutions. The performance of each method is evaluated by comparing the numerical solution to the exact solution using the Root Mean Square Error (RMSE) error measure. The results showed that the Euler method had the lowest accuracy rate, while the RK4 method produced significantly more accurate results. The RKF method performed best with small errors.