Analyzing Transient Response of Series RLC Circuit using Numerical Methods

Transient phenomena, resulting from abrupt changes in currents and voltages during switching events, are commonly encountered in circuits. RLC circuits, comprising resistors, inductors, and capacitors arranged in parallel, series, or combinations thereof, offer a suitable framework for studying these transients. Various damping factors inherent in the circuit dictate the unique nature of transient responses. To optimize numerical methods for transient analysis in RLC circuits, we compare Euler's method, Heun's method, and the Fourth-order Runge-Kutta (RK4) method against analytical solutions. Specifically focusing on series RLC circuits, we evaluate the Fourth-order Runge-Kutta (RK4) method and Butcher's fifth-order Runge-Kutta (BRK5) method. Our analysis involves comprehensive examination, visualization, and meticulous error analysis of numerical solutions obtained from these methods under different damping conditions. We aim to identify the most proficient method for accurate approximations in transient analysis. Through in-depth comparison, Butcher's fifth-order Runge-Kutta (BRK5) method emerges as superior in accuracy compared to the Fourth-order Runge-Kutta (RK4) method. This superiority is attributed to BRK5's advanced numerical techniques, enabling precise capture of transient responses in series RLC circuits. Our research underscores the importance of selecting appropriate numerical methods based on damping ratios, contributing to a deeper understanding of transient analysis in RLC circuits and its practical implications.