Visualization, Formulation and Intuitive Explanation of Iterative Methods for Transient Analysis of RLC Circuit

Abstract

The time-varying currents and voltages resulting from the sudden application of sources usually due to switching are transients. An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The transient response is dependent on the value of the di erent characteristics of the damping factor (i.e., overdamped, critically damped, and underdamped). The numerical solutions of rst and second-order di erential equations with initial value problem (IVP) have been computed by using the Explicit (Forward) Euler method, Implicit (Backward) Euler method, Classical second-order (Heun's or RK2) method, Third-order Runge-Kutta (RK3) method, Fourth order Runge-Kutta method and Butchers fth-order Runge-Kutta (BRK5) method. The observation compares this numerical solution of ODEs obtained by the above-mentioned methods among them with the necessary visualization and analysis of the error. These iterative methods will be extended and implement to analyze the transient analysis of an RLC circuit. The superiority of these methods over one another has been examined. The Butcher's fth-order Runge-Kutta (BRK5) method is found to be the best numerical technique to solve the transient analysis due to its high accuracy of approximations. Moreover, we consider the possibility of discussing and analyze above mentioned iterative methods in the cases of di erent characteristics of damping factors. Di erent methods are used di erent iterative methods to analyze the transient analysis of an RLC circuit and compared among them. The consequences of this work lend some limelight to the modern approaches to solving complicated mathematical problems.