New Solution Method for Electrical Systems Represented by Ordinary Differential Equation - Bilgehan, Bulent; Eminaga, Bugce; Riza, Mustafa (World Scientific Publ Co Pte Ltd, 2016)
Electrical circuits based on linear and nonlinear modelling principles have difficulties to meet demands caused by a large amount of data generated and processed. The aim is to examine the existing models from bigeometric calculus point of view to obtain accuracy on the results. This work is an application of bigeometric Runge-Kutta (BRK4) method aiming to solve differential equations with nonzero initial condition. This type of work arises from applications where the systems are defined by ordinary differential equations such as noise, filter, audio, chaotic circuits, etc. Solutions to these types of equations are not always easy. The improvement in this work is obtained by introducing bigeometric calculus in the process of seeking a solution to differential equations. Different classes of input signals are applied as input to the system and processed to determine the accuracy of the output. The applicability is tested against the classical method called Runge-Kutta (RK4). Simulation results confirm the application of BRK4 method in electrical circuit analysis. The new method also provides better results for all types of input signals, i.e., linear, nonlinear, constant or Gaussian.
Keywords: Signal and systems processing; bigeometric calculus; bigeometric Runge-Kutta; ordinary differential equation; Runge-Kutta; chaotic circuit