| Abstract |
Many filters, power converters, AC electric motors
and their shaft mechanics are characterized by Hamiltonian
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.
The symmetric Euler algorithm is often confused with the
forward Euler and is thus quite unknown. An analytic formula
for the numerical stability of the symmetric Euler algorithm
is presented. Accuracy of the forward Euler, backward
Euler, trapezoidal and symmetric Euier algorithms is
compared. Some applications are presented in detail. |
