doi: 10.17706/ijapm.2017.7.2.128-133
<i>L</i><sub>0</sub> Stable Trigonometrically Fitted Block Backward Differentiation Formula of Adams Type for Autonomous Oscillatory Problems
Solomon A. Okunuga
,
- Department of Mathematics, University of Lagos, Lagos, Nigeria
Abstract
In this paper, a <i>L</i><sub>0</sub> Stable Second Derivative Trigonometrically Fitted Block Backward Differentiation Formula of Adams Type (SDTFF) of algebraic order 4 is presented for the solution of autonomous oscillatory problems. A Continuous Second Derivative Trigonometrically Fitted (CSDTF) whose coefficients depend on the frequency and step size is constructed using trigonometric basis function. The CSDTF is used to generate the main method and one additional method which are combined and applied in block form as simultaneous numerical integrators. The stability properties of the method are investigated using boundary locus plot. It is found that the method is zero stable, consistent and hence converges. The method is applied on some numerical examples and the result show that the method is accurate and efficient.
Keywords
- Autonomous oscillatory problems
- backward differentiation formula
- continuous scheme
- trigonometrically fitted methods
How to Cite
Solomon A. Okunuga and R. I. Abdulganiy, "<i>L</i><sub>0</sub> Stable Trigonometrically Fitted Block Backward Differentiation Formula of Adams Type for Autonomous Oscillatory Problems," International Journal of Applied Physics and Mathematics, vol. 7, no. 2, pp. 128-133, 2017. https://doi.org/ 10.17706/ijapm.2017.7.2.128-133
Copyright & License
Copyright © 2017 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).