Application of the Runge-Kutta Fourth Order (RK4) and Runge-Kutta Fifth Order (RK5) in dynamic systems: a focus on electrical circuit analysis

This study examines the application of the Runge-Kutta Fourth Order (RK4) and Runge-Kutta Fifth Order (RK5) numerical methods in analyzing dynamic electrical systems, with a particular focus on both series and parallel RLC circuits. These numerical techniques are renowned for their ability to solve ordinary differential equations (ODEs) with a high level of accuracy and computational efficiency, especially in scenarios where analytical solutions are difficult or impossible to derive. The research aims to compare the effectiveness of RK4 and RK5 in simulating the transient and steady-state behaviours of electrical circuits under various damping conditions, including underdamped, overdamped, and critically damped responses. The study employs Mathematica as the primary tool to compare the accuracy of RK4 and RK5 in simulating both the transient (short-term) and steady-state (long-term) responses of electrical circuits under various damping conditions. The performance of each method is evaluated based on accuracy, stability, and computational efficiency. The results show that RK4 is a solid choice for balancing simplicity and performance, while RK5 stands out for its higher accuracy, especially important in situations where precision matters most. By applying both methods to series and parallel circuit setups, the study gives a more complete picture of how these numerical approaches perform in real-world circuit analysis. Overall, this work helps engineers, researchers, and students make better decisions about which method to use based on the type of circuit and how precise the simulation needs to be. It highlights the trade-offs between RK4 and RK5 and shows how choosing the right method can improve the accuracy and efficiency of electrical circuit modelling.