An accurate five-step trigonometrically-fitted numerical scheme for approximating solutions of second order ordinary differential equations with oscillatory solutions

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Authors :

Adebayo O. Adeniran 1 , Saheed O. Akindeinde 2 and Babatunde S. Ogundare 2*

Author Address :

1 Department of General Studies, Federal Polytechnic, Ile-Oluji, Nigeria.
2 Research Group in Computational Mathematics (RGCM), Department of Mathematics, Obafemi Awolowo University, 220005 Ile-Ife, Nigeria.

*Corresponding author.

Abstract :

In this paper, class of second order ordinary differential equation with oscillatory solutions is considered. By employing the trigonometric basis function, a continuous five-step scheme known as five-step trigonometrically fitted scheme is derived to approximate solutions to the class of considered equation. Consistency and zero stability of the developed method were proved. Stability and convergence properties of this new scheme were also established. The scheme so obtained is used to solve standard initial value problems with oscillatory solutions. From the numerical results obtained, it was revealed that the proposed method performs better than some of the existing methods in the literature.

Keywords :

Continuous schemes, Multistep collocation, Trigonometrically fitted method, Initial value problem.



Article Info :

Received : July 16, 2018; Accepted : September 13, 2018.



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