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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 '' +(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.
65L99Numerical methods for ODE
34A45Theoretical approximation of solutions of ODE
34C25Periodic solutions of ODE
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