Taylor Series Based Integration in Electric Circuits Simulations

Anotace: This paper deals with the extremely precise, stable and fast solution of the ordinary differential equations. The solution of these is performed using a method based on the Taylor series - The Modern Taylor Series Method. The paper investigates two problems to demonstrate the positive properties of the method: linear problem - the behavior of signal transmission on the telegraph line and a non-linear problem - the Van der Pol oscillator. Both problems were analyzed and solved using newly implemented MATLAB Modern Taylor Series Method solvers. The results were then compared to the state-of-the-art MATLAB solvers.