Numerical Approximations Techniques for Transient Analysis in LCR Circuits - Kafle, Jeevan; K. C., Manoj; Bhandari, Indra Bahadur (The Nepali Mathematical Sciences Report, 2025)
There are abundant real world problems in this nature which are governed by differential equations. They are usually non-linear in nature and due to its high complexity, obtaining the analytical solution is very hard or almost impossible. So, we widely use the numerical techniques to approximate the solutions. Likewise, Transient Analysis of an LCR electrical circuit is one of them. LCR circuit encompasses three different elements, i.e. Inductor (L), Capacitor (C) and Resistor (R). In this paper, we mainly discuss three major numerical techniques viz. Euler (Forward), fourth-order Runge-Kutta (RK4) and sixth-order Runge-Kutta (RK6) methods to approximate the numerical solutions of second-order differential equation of LCR circuit. Moreover, we compare the numerical solutions with exact solutions with necessary visualization. Concerning the various damping factor values, we discuss the damping conditions and consider the further possibility of discussion and analysis of this numerical methods.