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 and some relation equations of motion on the pivot vertically for arbitrary angles are obtained. The analytical approximation is derived in terms of the Jacobi ellip...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5454685 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558387610517504 |
|---|---|
| author | M.R. Alharthi Alvaro H. Salas Wedad Albalawi S.A. El-Tantawy |
| author_facet | M.R. Alharthi Alvaro H. Salas Wedad Albalawi S.A. El-Tantawy |
| author_sort | M.R. Alharthi |
| collection | DOAJ |
| description | In this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation and some relation equations of motion on the pivot vertically for arbitrary angles are obtained. The analytical approximation is derived in terms of the Jacobi elliptic functions with arbitrary elliptic modulus. For the numerical approximations, the Chebyshev collocation numerical method is introduced for analyzing the equation of motion. Moreover, the analytical approximation and numerical approximation using the Chebyshev collocation numerical method and the MATHEMATICA command Fit are compared with the Runge–Kutta (RK) numerical solution. Also, the maximum distance error to all obtained approximations 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. |
| format | Article |
| id | doaj-art-5dc27e7ce88f42d8ac29eb9473c14f5f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5dc27e7ce88f42d8ac29eb9473c14f5f2025-02-03T01:32:30ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5454685Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation MethodM.R. Alharthi0Alvaro H. Salas1Wedad Albalawi2S.A. El-Tantawy3Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematical SciencesDepartment of PhysicsIn this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation and some relation equations of motion on the pivot vertically for arbitrary angles are obtained. The analytical approximation is derived in terms of the Jacobi elliptic functions with arbitrary elliptic modulus. For the numerical approximations, the Chebyshev collocation numerical method is introduced for analyzing the equation of motion. Moreover, the analytical approximation and numerical approximation using the Chebyshev collocation numerical method and the MATHEMATICA command Fit are compared with the Runge–Kutta (RK) numerical solution. Also, the maximum distance error to all obtained approximations 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.http://dx.doi.org/10.1155/2022/5454685 |
| spellingShingle | M.R. Alharthi Alvaro H. Salas Wedad Albalawi S.A. El-Tantawy Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method Journal of Mathematics |
| title | Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method |
| title_full | Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method |
| title_fullStr | Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method |
| title_full_unstemmed | Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method |
| title_short | Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method |
| title_sort | novel analytical and numerical approximations to the forced damped parametric driven pendulum oscillator chebyshev collocation method |
| url | http://dx.doi.org/10.1155/2022/5454685 |
| work_keys_str_mv | AT mralharthi novelanalyticalandnumericalapproximationstotheforceddampedparametricdrivenpendulumoscillatorchebyshevcollocationmethod AT alvarohsalas novelanalyticalandnumericalapproximationstotheforceddampedparametricdrivenpendulumoscillatorchebyshevcollocationmethod AT wedadalbalawi novelanalyticalandnumericalapproximationstotheforceddampedparametricdrivenpendulumoscillatorchebyshevcollocationmethod AT saeltantawy novelanalyticalandnumericalapproximationstotheforceddampedparametricdrivenpendulumoscillatorchebyshevcollocationmethod |