Abstract
The relativistic harmonic oscillator equation is a nonlinear ordinary differential equation given by:
x
¨
+
(
1
-
x
˙
2
)
3
/
2
x
=
0
. In this paper, the differential transformation method (DTM) and a relatively new technique, known as aftertreatment technique, are proposed to obtain new approximate periodic solutions for the relativistic harmonic oscillator equation under the initial conditions
x
(
0
)
=
0
,
x
˙
(
0
)
=
β
.