Comparative Convergence Analysis of Runge- Kutta Fourth Order and Runge-Kutta-Fehlberge Methods Implementation in Matlab and Python Applied to a Series RLC Circuit

This research investigates the comparative convergence properties and computational efficiency of the Runge- Kutta Fourth Order (RK4) and Runge-Kutta Fehlberg (RKF) methods in solving a second-order differential equation modeling a series RLC circuit. The study is conducted using MATLAB and Python, focusing on the convergence properties of the Runge-Kutta fourth-order method and the Runge-Kutta Fehlberg method in approximating the solution of the given ODE. Key findings indicate that both RK4 and RKF methods are highly efficient in solving second-order differential equations, with the RKF method demonstrating superior efficiency. MATLAB and Python both provide robust environments for implementing the RK4 and RKF methods. MATLAB's built-in functions facilitate straightforward implementation, while Python’s libraries like SciPy, SymPy, Matplotlib, and Pandas offer additional flexibility and simplicity. Performance analysis shows that MATLAB establishes convergence in approximately ten seconds, whereas Python takes about two minutes. MATLAB generally offers faster computation for vectorized operations, which is advantageous for large-scale problems. Python, however, provides comparable performance with better integration capabilities for other software and tools. This research underscores the importance of choosing appropriate numerical methods for solving differential equations in electrical circuits, contributing valuable insights for students, researchers, and academicians in computational mathematics and engineering fields.