Application of He's Homotopy Perturbation Method to the Relativistic (An)harmonic Oscillator. II: A More Accurate Approximate Solution

摘要

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the behaviour of a relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. The approximate formulas obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation A. Only one iteration leads to high accuracy of the solutions and for any value of A and the discrepancy between the approximate frequency and the exact one never exceeds 1.6%.