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

Citation:
Adeniran, O, Ogundare B.  2018.  An accurate five-step trigonometrically-fitted numerical scheme for approximating solutions of second order ordinary differential equations with oscillatory solutions, 2018/11/14. 06

Abstract:

In this paper, class of second order ordinary differential equation with oscillatory solutions is considered. Byemploying 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.

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