Visualization, Formulation and Intuitive Explanation of Iterative Methods for Transient Analysis of RLC Circuit
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematics
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.
Description
Keywords
Resistor Inductor Capacitor, Intuitive explanation, Visualization, Transient analysis