Sufia  Zulfa Ahmad, Mohamed  Yousif Turki, Fudziah  Ismail, Norazak  Senu, 
    Extra Derivative Multistep Methods with Trigonometric-Fitting for
Oscillatory Problems,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 7,
    2019,
    Pages 2230-2239,
    ISSN 1816-949x,
    jeasci.2019.2230.2239,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.2230.2239)
    Abstract: A set of new linear multistep method of order three and four with extra derivatives are developed for
solving special second order ordinary differential equations. The extra derivatives are incorporated into the
methods, so that, a more accurate numerical results can be obtained. The methods are developed using the
sequence of Chebyshev polynomials as the basis function. The methods are then trigonometrically-fitted, so
that, they are suitable for solving highly oscillatory problems arise from the special second order ordinary
differential equations. Numerical experiments are carried out to show the efficiency and accuracy of the new
methods in comparison with methods in the literature.
    Keywords: Linear multistep method;collocation method;trigonometrically-fitted;oscillatory problems;accuracy;different equation