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Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method. (English) Zbl 1222.65084
Summary: The relativistic harmonic oscillator equation is a nonlinear ordinary differential equation given by ${x}^{\text{'}\text{'}}+{\left(1-{{x}^{\text{'}}}^{2}\right)}^{3/2}x=0$. 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 $x\left(0\right)=0$, ${x}^{\text{'}}\left(0\right)=\beta$.
##### MSC:
 65L99 Numerical methods for ODE 34A45 Theoretical approximation of solutions of ODE 34C25 Periodic solutions of ODE
##### References:
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