Awoyemi, D.O., Adebile, E.A., Adesanya, A.O. and Anake, T.A. (2011) Modified Block Method for the Direct Solution of Second Ordinary Differential Equations. International Journal of Pure and Applied Mathematics, 181-188.

has been cited by the following article:

• TITLE: A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations

  AUTHORS: Emmanuel Adegbemiro Areo, Micheal Temitope Omojola

  KEYWORDS: Power Series Approximate Solutions, Consistent, Zero Stability, Continuous Block Method, Dynamic Model

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.4, December 16, 2015

  ABSTRACT: In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.