Comparative Evaluation of RK4 and ABM4 Methods for Underdamped Transient Response Analysis of RLC Circuits

Abstract

The transient response of series RLC circuits in the underdamped regime displays oscillatory behavior that requires numerical method capable of preserving both amplitude and phase accuracy. This study aims to compare the numerical performance of two fourth-order integration methods, namely the classical Runge-Kutta method (RK4) and the Adams-Bashforth-Moulton predictor-corrector method (ABM4), in simulating the transient response of a series RLC circuit. The circuit dynamics are formulated as a system of first-order ordinary differential equations derived from Kirchhoff’s Voltage Law and solved numerically using both methods. The simulations are performed using practical circuit parameters representative of low-power AC systems and zero initial conditions. Numerical simulation is evaluated in terms of computational efficiency, global accuracy measured by root mean square error relative to the analytical solution, and local accuracy assessed through peakwise relative error at the first oscillation peak. The results show that ABM4 consistently requires less computational time than RK4 for the same number of time steps due to its multi-step formulation. However, RK4 provides smaller global and peakwise errors, indicating superior phase accuracy. These results highlight a trade-off between computational efficiency and numerical accuracy in underdamped RLC transient simulations.