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Home  >  Volume 28. No.1 (Nov. 2014)

17. A Sixth -Order Implicit Method for the Numerical Integration of Initial Value Problems of Third Order Ordinary Differential Equations by Awoyemi .D. O, Kayode S. J., and Adoghe, L.O. - Page 95-102
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In this paper we derive a linear multistep method  with step number =  using Taylor series as basis function for approximate solution .An order six scheme 

is produced which is used for the direct solution of third order initial value problems in ordinary differential equation . Taylor’s seriesalgorithm of the same order was developed to implement our method. This implementation strategy is found to be 

efficient and more accurate as the result has shownin the numerical experiments. 

Keywords:Linear multistep methods, third order, Taylor series, approximate solutions, direct solution basis function