Optimal analytical and numerical approximations to the(un)forced(un)damped parametric pendulum oscillator  

作　　者：Haifa A Alyousef M R Alharthi Alvaro H Salas S A El-Tantawy 

机构地区：[1]Department of physics,College of Science,Princess Nourah bint Abdulrahman University,P.O.Box 84428,Riyadh 11671,Saudi Arabia [2]Department of Mathematics and Statistics,College of Science,Taif University,P.O.Box 11099,Taif 21944,Saudi Arabia [3]Department of Mathematics and Statistics,Universidad Nacional de Colombia,FIZMAKO Research Group,Sede Manizales,Colombia [4]Department of Physics,Faculty of Science,Port Said University,Port Said 42521,Egypt [5]Research Center for Physics(RCP),Department of Physics,Faculty of Science and Arts,Al-Mikhwah,Al-Baha University,Saudi Arabia

出　　处：《Communications in Theoretical Physics》2022年第10期16-29,共14页理论物理通讯（英文版）

基　　金：The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project (Grant No. PNURSP2022R17);Taif University Researchers supporting project number (TURSP2020/275), Taif University, Taif, Saudi Arabia。

摘　　要：The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions.In the second approach,some approximations to(un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method.In the third approach,He’s frequency-amplitude principle is applied for deriving some approximations to the(un)damped PPO.In the forth approach,He’s homotopy technique is employed for analyzing the forced(un)damped PPO numerically.In the fifth approach,the p-solution Method,which is constructed based on Krylov–Bogoliúbov Mitropolsky method,is introduced for deriving an approximation to the forced damped PPO.In the final approach,the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically.All proposed techniques are compared to the fourth-order Runge–Kutta(RK4)numerical solution.Moreover,the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations.The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science,e.g.waves and oscillations in plasma physics.

关 键 词：parametric pendulum equation Ansatz method He’s frequency-amplitude principle He’s homotopy technique Krylov-Bogoliúbov Mitropolsky method the hybrid Padé-finite difference method 

分 类 号：O302[理学—力学]