British Journal of Mathematics & Computer Science 17(5): 1-10, 2016, Article no.BJMCS.25243 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org Boundary Value Technique for Initial Value Problems with Continuous Third Derivative Multistep Method of Enright I. O. Longe 1 and A. O. Adeniran 1 ∗ 1 Department of Statistics, The Federal Polytechnic, Ile-Oluji, Nigeria. Authors’ contributions This work was carried out in collaboration between both authors. Author IOL proposed the algotithms, author AOA developed, analysed and implemented the method. Authors IOL and AOA drafted the manuscripts. Both authors read and approved the final manuscript. Article Information DOI: 10.9734/BJMCS/2016/25243 Editor(s): (1) Jinyun Yuan, Department of Mathematics, Federal University of Parana, Brazil. Reviewers: (1) Mostafa M. A. Khater, Mansoura University, Egypt. (2) Asha Ram Gairola, University of Petroleum and Energy Studies Dehradun, India. Complete Peer review History: http://sciencedomain.org/review-history/15412 Received: 24 th February 2016 Accepted: 18 th April 2016 Original Research Article Published: 17 th July 2016 Abstract 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. Keywords: Continuous schemes; multistep collocation; stiff system; initial value problem. Mathematics Subject Classification (2000): Primary 65L05 Secondary 65L06. *Corresponding author: E-mail: dareadeniran2007@yahoo.com;