P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-27
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Some new higher algebraic order symmetric various-step methods are introduced.
For these methods a direct formula for the computation of the phase-lag is given.
Basing on this formula, calculation of free parameters is performed to minimize the phase-lag.
An explicit symmetric multistep method is presented.
This method is of higher algebraic order and is fitted both exponentially and trigonometrically.
Such methods are needed in various branches of natural science, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior.
Many exponentially-fitted symmetric multistepmethods for the second-order differential equation are already developed.
The stability properties of several existing methods are analyzed, and a new P-stable method is proposed, to establish the existence of methods to which our definition applies and to demonstrate its relevance to stiff oscillatory problems.
The work is mainly concerned with two-stepmethods but extensions tomethods of larger step-number are also considered.
To have an idea about its accuracy, we examine their phase properties.
The efficiency of the proposed method is demonstrated by its application to well-known periodic orbital problems.
The new methods showed better stability properties than the previous ones.
American Psychological Association (APA)
Hendi, Fatheah A.. 2011. P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-469654
Modern Language Association (MLA)
Hendi, Fatheah A.. P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations. Journal of Applied Mathematics No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-469654
American Medical Association (AMA)
Hendi, Fatheah A.. P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-469654
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-469654