Assessing the Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Forced and damped oscillators appear in the mathematical modelling of many problems in pure
and applied sciences such as physics, engineering and celestial mechanics among others.
Although the accuracy of the T{functions series method is high the calculus of their coecients
needs specic recurrences in each case.
To avoid this inconvenience the T{functions series method is transformed into a multistep method
whose coecients are calculated using recurrence procedures. These methods are convergent and
have the same properties to the T{functions series method.
Numerical examples already used by other authors are presented, such as, a sti problem, a Dung
oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics
J2.