Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods

In this work, some new approximate solutions to the damped pendulum equation are obtained. In addition, the Newton–Raphson method (NRM), moving boundary method, and fourth-order Runge Kutta forth-order (RK4) are introduced to analyze the problem under study numerically. With respect to the approxima...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Wedad Albalawi, Alvaro H. Salas, S. A. El-Tantawy, Amr Abd Al-Rahman Youssef
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2021
Materias:	pendulum equation damped oscillator jacobi elliptic functions period of oscillations chaos Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/b6419f8a7cee4546b15d9d72634fc67a
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b6419f8a7cee4546b15d9d72634fc67a
record_format	dspace
spelling	oai:doaj.org-article:b6419f8a7cee4546b15d9d72634fc67a2021-11-26T11:19:47ZApproximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods1658-365510.1080/16583655.2021.1989739https://doaj.org/article/b6419f8a7cee4546b15d9d72634fc67a2021-01-01T00:00:00Zhttp://dx.doi.org/10.1080/16583655.2021.1989739https://doaj.org/toc/1658-3655In this work, some new approximate solutions to the damped pendulum equation are obtained. In addition, the Newton–Raphson method (NRM), moving boundary method, and fourth-order Runge Kutta forth-order (RK4) are introduced to analyze the problem under study numerically. With respect to the approximate analytic solutions, two schemes are devoted: in the first approach, we can solve our problem with specific values for the initial conditions (zero initial angle) and after that compare our analytic solution with numerical solutions and with some published solutions. Thereafter, some modifications and improvements for the analytic solution will be constructed in order to get high-accurate solutions. With respect to the second scheme, we can solve our problem with arbitrary initial conditions and then make a comparison between the obtained results and the mentioned numerical solutions. Moreover, the distance error for all obtained solutions is estimated with respect to the RK4 solution.Wedad AlbalawiAlvaro H. SalasS. A. El-TantawyAmr Abd Al-Rahman YoussefTaylor & Francis Grouparticlependulum equationdamped oscillatorjacobi elliptic functionsperiod of oscillationschaosScience (General)Q1-390ENJournal of Taibah University for Science, Vol 15, Iss 1, Pp 479-485 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	pendulum equation damped oscillator jacobi elliptic functions period of oscillations chaos Science (General) Q1-390
spellingShingle	pendulum equation damped oscillator jacobi elliptic functions period of oscillations chaos Science (General) Q1-390 Wedad Albalawi Alvaro H. Salas S. A. El-Tantawy Amr Abd Al-Rahman Youssef Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
description	In this work, some new approximate solutions to the damped pendulum equation are obtained. In addition, the Newton–Raphson method (NRM), moving boundary method, and fourth-order Runge Kutta forth-order (RK4) are introduced to analyze the problem under study numerically. With respect to the approximate analytic solutions, two schemes are devoted: in the first approach, we can solve our problem with specific values for the initial conditions (zero initial angle) and after that compare our analytic solution with numerical solutions and with some published solutions. Thereafter, some modifications and improvements for the analytic solution will be constructed in order to get high-accurate solutions. With respect to the second scheme, we can solve our problem with arbitrary initial conditions and then make a comparison between the obtained results and the mentioned numerical solutions. Moreover, the distance error for all obtained solutions is estimated with respect to the RK4 solution.
format	article
author	Wedad Albalawi Alvaro H. Salas S. A. El-Tantawy Amr Abd Al-Rahman Youssef
author_facet	Wedad Albalawi Alvaro H. Salas S. A. El-Tantawy Amr Abd Al-Rahman Youssef
author_sort	Wedad Albalawi
title	Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
title_short	Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
title_full	Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
title_fullStr	Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
title_full_unstemmed	Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods
title_sort	approximate analytical and numerical solutions to the damped pendulum oscillator: newton–raphson and moving boundary methods
publisher	Taylor & Francis Group
publishDate	2021
url	https://doaj.org/article/b6419f8a7cee4546b15d9d72634fc67a
work_keys_str_mv	AT wedadalbalawi approximateanalyticalandnumericalsolutionstothedampedpendulumoscillatornewtonraphsonandmovingboundarymethods AT alvarohsalas approximateanalyticalandnumericalsolutionstothedampedpendulumoscillatornewtonraphsonandmovingboundarymethods AT saeltantawy approximateanalyticalandnumericalsolutionstothedampedpendulumoscillatornewtonraphsonandmovingboundarymethods AT amrabdalrahmanyoussef approximateanalyticalandnumericalsolutionstothedampedpendulumoscillatornewtonraphsonandmovingboundarymethods
_version_	1718409557135327232

Approximate analytical and numerical solutions to the damped pendulum oscillator: Newton–Raphson and moving boundary methods

Ejemplares similares