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 Fifth Order (RK5) numerical methods in modelling dynamic electrical systems, focusing on series and parallel RLC circuits. Both approaches are widely recognized for solving ordinary differential equations (ODEs) with accuracy and efficiency, making them valuable when analytical solutions are difficult to obtain. The research compares the performance of RK4 and RK5 in simulating transient and steady-state behaviours under different damping conditions, including underdamped, overdamped, and critically damped cases. Mathematica was used as the computational platform to evaluate each method in terms of accuracy, stability, and computational cost. Findings show that RK4 offers a practical balance between simplicity and performance, making it suitable for general circuit analysis. In contrast, RK5 demonstrates superior precision, especially in scenarios where high accuracy is essential. By applying both methods to different circuit configurations, the study provides a well-rounded understanding of their capabilities and limitations in real-world applications. Overall, the results highlight the trade-offs between RK4 and RK5, offering engineers, researchers, and students clearer guidance in selecting the most suitable method. Choosing the appropriate approach enhances both the accuracy and efficiency of electrical circuit modelling.