Numerical higher-order Runge-Kutta methods in transient and damping analysis

Abstract

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 5th and Runge-Kutta 8th 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.