Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations

Complexity 2022:1-14 (2022)
  Copy   BIBTEX

Abstract

In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. Two different analytical approximations are obtained: for the first approximation, the ansatz method with the help of Chebyshev approximate polynomial is employed to derive an approximation in the form of trigonometric functions. For the second analytical approximation, a novel hybrid homotopy with Krylov–Bogoliubov–Mitropolsky method is introduced for the first time for analyzing the evolution equation. For the numerical approximation, both the finite difference method and Galerkin method are presented for analyzing the strong nonlinear quadratically damped pendulum equation that arises in real life, such as nonlinear phenomena in plasma physics, engineering, and so on. Several examples are discussed and compared to the Runge–Kutta numerical approximation to investigate and examine the accuracy of the obtained approximations. Moreover, the accuracy of all obtained approximations is checked by estimating the maximum residual and distance errors.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On the presumed superiority of analytical solutions over numerical methods.Vincent Ardourel & Julie Jebeile - 2017 - European Journal for Philosophy of Science 7 (2):201-220.
Approximations and truth spaces.Jean-Pierre Marquis - 1991 - Journal of Philosophical Logic 20 (4):375 - 401.
The pendulum: A paradigm for the linear oscillator.Ronald Newburgh - 2004 - Science & Education 13 (4-5):297-307.
The Psychophysics of the Chervreul Hand-Held Pendulum.R. S. Kaushal - 2016 - Journal of Consciousness Studies 23 (9-10):134-152.

Analytics

Added to PP
2022-05-29

Downloads
3 (#1,519,925)

6 months
2 (#668,348)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references