Numerical analysis of a fractal modification of Yao–Cheng oscillator

Abstract

In this paper, a numerical approach based on the two-scale fractal transformation and the global residue harmonic balance method (called as TSFT-GRHBM), is proposed for finding the approximated solutions of a fractal modification of Yao–Cheng oscillator with He’s fractal derivative. The approximated frequency for the classical Yao–Cheng oscillator is given. The approximations with high accuracy for the fractal or classical Yao–Cheng oscillator are also presented, and compared with Runge–Kutta method (RK). The numerical sensitive analysis of the approximations is further considered with respect to different amplitudes and parameters. Numerical results confirm the efficiency and stability of this method.

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