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

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