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 different characteristics of damping factor (i.e., over damped, critically damped and under damped). We have computed the numerical solutions of second order differential equation with initial value problem (IVP) by using Explicit (Forward) Euler method, Third order Runge-Kutta (RK3) methods and Butchers fifth order Runge-Kutta (BRK5). The observation compares this numerical solution of ODEs obtained by above-mentioned methods among them with necessary visualization and analysis of the error. These iterative methods will be extended and implement to analyze the transient analysis of an RLC circuit.  We have examined the superiority of those methods over one another. The Butchers fifth 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 discussion and analyze above mentioned iterative methods in the cases of different characteristics of damping factor. BIBECHANA 18 (2) (2021) 9-17

A sudden application of sources results in time-varying currents and voltages in the circuit known as transients. This phenomenon occurs frequently during switching. A simple circuit constituting a resistor, an inductor, and a capacitor is termed an RLC circuit. It may be in parallel or series configuration or both. Different values of damping factors determine the different nature of the transient response. We applied different numerical solution methods such as explicit (forward) Euler method, third-order Runge-Kutta (RK3) method, and Butcher's fifth-order Runge-Kutta (BRK5) method to approximate the solution of second-order differential equation with initial value problem (IVP). We thoroughly compared the numerical solutions obtained by these methods with the necessary visualization and analysis of error. We also examined the superiority of these methods over one another and the appropriateness of numerical methods for different damping conditions is explored. With high accuracy of the approximation and thorough analysis of the observation, we found Butcher's fifth-order Runge-Kutta (BRK5) method to be the best numerical technique. Regarding the different values of damping factors, we considered the further possibility of discussion and analysis of this iterative method.

Many physical problems in the real world are frequently modeled by ordinary differential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider different numerical methods viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s method or Improved Euler method), Third-order Runge-Kutta (RK3) method, Fourth-order Runge-Kutta (RK4) method, and Butcher fifth-order Runge-Kutta (BRK5) method which are popular classical iteration methods of approximating solutions of ODEs. Moreover, an intuitive explanation of those methods is also be presented, comparing among them and also with exact solutions with necessary visualizations. Finally, we analyze the error and accuracy of these methods with the help of suitable mathematical programming software.