# A Robust Block Hybrid Trigonometric Method for the Numerical Integration of Oscillatory Second Order Nonlinear Initial Value Problems

A Robust Block Hybrid Trigonometric Method for the Numerical Integration of Oscillatory Second Order Nonlinear Initial Value Problems

R. I. Abdulganiy O.A. Akinfenwa S.A. Okunuga G. O. Oladimeji

Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria

Corresponding Author Email:
profabdulcalculus@gmail.com, akinolu35@yahoo.com, sokunuga@unilag.edu.ng, Ganiyu_opeyemi@yahoo.com
Page:
497-518
|
DOI:
https://doi.org/10.18280/ama_a.540404
17 December 2017
|
Accepted:
30 December 2017
|
Published:
31 December 2017
| Citation

OPEN ACCESS

Abstract:

A new Block Hybrid Trigonometrically Fitted Method (BHTM) for the numerical integration of second order nonlinear initial value problems with oscillatory solutions is presented in this paper. The BHTM is based on multistep collocation method. The examination of the stability properties of the method shows that it is A-stable. Numerical experiments are carried out to show the accuracy and efficiency of the method on second order nonlinear initial value problems with oscillatory solutions.

Keywords:

Collocation, Hybrid, Nonlinear Second Order IVPs, Trigonometrically Fitted.

1. Introductions
2. Derivation of the Method
3. Analysis of BTHM
4. Numerical Examples
5. Conclusion
Acknowledgment

The authors would like to thank the Nigeria TETFUND for the research grant given towards this research work.

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