Boundary Value Technique for Initial Value Problems with Continuous Third Derivative Multistep Method of Enright

The Enright's third derivative method which is A-stable is derived using multistep collocation approach. The continuous method so obtained are use to generate the main method and the complementary methods to solve standard problems via boundary value techniques such that the numerical solution of a problem is obtained on the domain of integration simultaneously. Numerical result obtained via the implementation of the methods shows that the new method can compete with the existing ones (Enright [1], Ehigie, Jator, Sofolowe and Okunuga [2], Jator-Sahi [3] , Wu-Xia [4]) in the literature.