Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method

The relativistic harmonic oscillator equation is a nonlinear ordinary differential equation given by: x¨+(1-x˙2)3/2x=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.