Fast and accurate symmetric euler algorithm for electromechanical simulations

Many filters, power converters, AC electric motors and their shaft mechanics are characterized by even order differential equation systems that are oscillatory in their nature. The low damping causes problems with the accuracy of both the forward and the backward Euler algorithms. However, the symmetric Euler algorithm, which is even simpler than the forward Euler, gives an accuracy that is comparable to the accuracy obtained by the trapezoidal method without requiring matrix inversion. The symmetric Euler algorithm is often confused with the forward Euler and is thus quite unknown. A formula for the numerical stability of the symmetric Euler algorithm is presented. Accuracies of the forward Euler, backward Euler, modified Euler, trapezoidal, Runge-Kutta and symmetric Euler algorithms are compared. Some applications are presented in detail.