A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-22
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs).
Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point.
We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods.
The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.
American Psychological Association (APA)
Ngwane, Fidele& Jator, S. N.. 2017. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems. International Journal of Differential Equations،Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1165885
Modern Language Association (MLA)
Ngwane, Fidele& Jator, S. N.. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems. International Journal of Differential Equations No. 2017 (2017), pp.1-14.
https://search.emarefa.net/detail/BIM-1165885
American Medical Association (AMA)
Ngwane, Fidele& Jator, S. N.. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems. International Journal of Differential Equations. 2017. Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1165885
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1165885