Error Free Butcher Algorithms for Linear Electrical Circuits

In this paper, an error‐free Butcher algorithm is introduced to study the singular system of a linear electrical circuit for time invariant and time varying cases. The discrete solutions obtained using Runge‐Kutta (RK)‐Butcher algorithms are compared with the exact solutions of the electrical circuit problem and are found to be very accurate. Stability regions for the single term Walsh series (STWS) method and the RK‐Butcher algorithm are presented. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of the RK‐Butcher algorithm. This RK‐Butcher algorithm can be easily implemented in a digital computer for any singular system of electrical circuits.