Representation of the poincaré sections via dormand–prince8 (5, 3) algorithm
Author
Source
Journal of Basrah Researches : Sciences
Issue
Vol. 33, Issue 3A (30 Sep. 2007), pp.8-23, 16 p.
Publisher
University of Basrah College of Education for Pure Sciences
Publication Date
2007-09-30
Country of Publication
Iraq
No. of Pages
16
Main Subjects
Topics
Abstract AR
استخدمنا خوارزمية (3، 5) Dormand-Prince8 لتحليل نظامين كلاسيكيين لا خطيين، و هما البندول المتضائل بارامتريا و المتذبذب المساق المتضائل و تمثيل مقاطع (Poincaré) بطريقتين مختلفتين.
توضح التغيرات في حالة النظام وفق شـروط ابتدائية مختارة مــن خـلال حوض الجـذب للنظام.
الخوارزميات المسـتخدمة هنا تعطي حلولا غير مسـتقرة للنظامين قيد الدراسة.
خوارزمية Dormand-Prince أظهرت حلولا مستقرة لقيم كبيرة من شرائح التكامل الزمني، بالمقارنة مع بقية الخوارزميات.
Abstract EN
This paper deals with the Dormand-Prince 8(5, 3) algorithm to analyze two classical nonlinear systems, namely the parametrically damped pendulum and driven damped oscillator, and represents the Poincaré sections in two different ways.
The basin of attraction illustrates the changing of the status for the system according to the choosing of the initial conditions.
Many of algorithms like Euler, Runge-Kutta 2 & 4, Runge-Kutta Fehlberg, Extrapolation, Cash-Karp, Adams-Bashforth-Moulton4, Gear & Implicit Gear, Hamming, Milne and Heun show unstable solutions for our systems.
The Dormand-Prince8 (5, 3) algorithm shows a stable solution for big values of integration step size of the time, in comparison with other algorithms.
American Psychological Association (APA)
Imarah, Ali Ahmad. 2007. Representation of the poincaré sections via dormand–prince8 (5, 3) algorithm. Journal of Basrah Researches : Sciences،Vol. 33, no. 3A, pp.8-23.
https://search.emarefa.net/detail/BIM-382259
Modern Language Association (MLA)
Imarah, Ali Ahmad. Representation of the poincaré sections via dormand–prince8 (5, 3) algorithm. Journal of Basrah Researches : Sciences Vol. 33, no. 3A (Sep. 2007), pp.8-23.
https://search.emarefa.net/detail/BIM-382259
American Medical Association (AMA)
Imarah, Ali Ahmad. Representation of the poincaré sections via dormand–prince8 (5, 3) algorithm. Journal of Basrah Researches : Sciences. 2007. Vol. 33, no. 3A, pp.8-23.
https://search.emarefa.net/detail/BIM-382259
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-382259