Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations
Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.
 S. O. Fatunla, Block Method for Second Order Initial Value Problem. International Journal of Computer Mathematics, England. Vol. 4, 1991, pp 55 – 63.
 S. O. Fatunla, Higher Order parallel Methods for Second Order ODEs. Proceedings of the fifth international conference on scientific computing, 1994, pp 61 –67.
 D. Garity, http://www.math.oregonstate.edu/ Department of Mathematics, Oregon State University Corvallis. Retrieved on 13th November, 2013.
 J. D. Lambert, Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA, 1973).
 P. Onumanyi, D.O. Awoyemi, S.N. Jator and U.W. Sirisena, New linear Multistep with Continuous Coefficient for first order initial value problems. Journal of Mathematical Society, 13, 1994, pp 37 – 51.
 G.U. Agbeboh, C.A. Esekhaigbe, and L.A. Ukpebor, On the Coefficient Analysis of a Modified Sixth Stage – Fourth Order Runge – Kutta Formula for Solving Initial Value Problems (ivp¬¬¬¬¬¬¬s¬). Int. J. Num Maths. Vol. 5 N0. 2, 2010, pp. 204 – 221.
 J. Sunday and M.R. Odekunle, A New Numerical Integrator for the Solution of Initial Value Problems inOrdinary Differential Equations. Pacific Journal of Science and Technology, Vol. 13 N0. 1, 2012, pp. 221 – 227.
 P. Henrici, Discrete Variable Methods for ODEs. (John Willey New York U.S.A, 1962).