Approximate Solutions to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Numerical Solution

Abstract

In this work, novel semi-analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation on the pivot vertically for arbitrary angles are obtained for the first time. The semi-analytical solution is derived in terms of the Jacobi elliptic functions with arbitrary elliptic modulus. For the numerical analysis, the Chebyshev collocation numerical method is introduced for analyzing tthe forced damped parametric driven pendulum equation. Moreover, the semi-analytical solution and Chebyshev collocation numerical solution are compared with the Runge-Kutta (RK) numerical solution. Also, the maximum distance error to the obtained approximate solutions is estimated with respect to the RK numerical solution. The obtained results help many authors to understand the mechanism of many phenomena related to the plasma physics, classical mechanics, quantum mechanics, optical fiber, and electronic circuits.

Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method

“…is paper was only published as a preprint entitled Approximate Solutions to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Numerical Solution [34].…”