International Journal of Advanced and Applied Sciences, 9(10) 2022, Pages: 174-179 Contents lists available at Science-Gate International Journal of Advanced and Applied Sciences Journal homepage: http://www.science-gate.com/IJAAS.html 174 Numerical higher-order Runge-Kutta methods in transient and damping analysis A. G. Shaikh 1, *, U. Keerio 2 , Wajid Shaikh 3 , A. H. Sheikh 4 1 Department of BS & RS, QUEST, Nawabshah, Pakistan 2 Department of Electrical Engineering, QUEST, Nawabshah, Pakistan 3 Department of Mathematics & Statistics, QUEST, Nawabshah, Pakistan 4 Institute of Business Management (IOB), Karachi, Pakistan ARTICLE INFO ABSTRACT Article history: Received 23 July 2021 Received in revised form 31 January 2022 Accepted 18 July 2022 Transient analysis of an RLC circuit (or LCR circuit) comprising of a resistor, an inductor, and a capacitor are analyzed. Kirchhoff’s voltage and current laws were used to generate equations for voltages and currents across the elements in an RLC circuit. From Kirchhoff’s law, the resulting first-order and second-order differential equations, The different higher-order Runge-Kutta methods are applied with MATLAB simulations to check how changes in resistance affect transient which is transitory bursts of energy induced upon power, data, or communication lines; characterized by extremely high voltages that drive tremendous amounts of current into an electrical circuit for a few millionths, up to a few thousandths, of a second, and are very sensitive as well important their critical and careful analysis is also very important. The Runge-Kutta 5 th and Runge-Kutta 8 th order methods are applied to get nearer exact solutions and the numerical results are presented to illustrate the robustness and competency of the different higher-order Runge-Kutta methods in terms of accuracy. Keywords: RLC circuit Numerical methods Runge-Kutta MATLAB Damping © 2022 The Authors. Published by IASE. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction *The transient analysis in the circuits and how the basic circuit elements like a resistor, capacitor, and inductor behave in the transient is of great importance (Das, 2010). Whenever we switch on the power supply in the circuit or turn off the supply or anything in the circuit changes abruptly, then the circuit takes some time to respond to this new condition and attain new steady state values. During the circuit operation, if anything or any parameter changes abruptly due to some surge or spike, then due to these abrupt changes, there could be a circuit failure or components failure. In addition, to investigate this failure one needs to look into the transient analysis that how voltage and current across the circuit elements changes during this transient. So, if we do the transient analysis then we can design the circuit in such a way that it can withstand such abrupt changes. Apart from circuit * Corresponding Author. Email Address: agshaikh@quest.edu.pk (A. G. Shaikh) https://doi.org/10.21833/ijaas.2022.10.020 Corresponding author's ORCID profile: https://orcid.org/0000-0001-7367-993X 2313-626X/© 2022 The Authors. Published by IASE. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) stability and failure analysis, in switching applications also this transient analysis is quite helpful. Transient normally results in changing the state of the components of an electrical circuit. It is very difficult for the capacitor voltage and the inductor current in an electrical circuit to assume a new steady state value. Transient analysis is very important since it can be used in analyzing the performance of any electrical circuit (Kee and Ranom, 2018). Thus, for an electrical current or voltage flowing through an electrical circuit, there can be various forms of the voltage or current. Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL) are normally in the form of differential equations rather than algebraic equations, these differential equations are not easily solved analytically when the order is high and complex. The numerical or approximate methods are one of the best techniques in solving almost all mathematical equations. The Runge-Kutta method was by far and away, the world's most popular numerical method for over 100 years, therefore the use of particular iterative methods depends on their efficiency. The efficiency of iterative methods depends on the stability, and cost in terms of time, suitability, and accuracy (Kafle et al., 2021). Without the use of the most accurate method, one might not be able to get an accurate solution and this might affect further