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In this paper we derived a continuous linear multistep method (LMM) with step number k = 5 through collocation and interpolation techniques using power series as basis function for approximate solution. An order nine p-stable scheme is developed which was used to solve the third order initial value problems in ordinary differential equation without first reducing to a system of first order equations. Taylor's series algorithm of the same order was developed to implement our method. The resultdoi:10.4236/ajcm.2014.43011 fatcat:xbmarvmfqzdwva7salf7jlydfm