A Class of Implicit Six Step Hybrid Backward Differentiation Formulas for the Solution of Second Order Differential Equations
Umaru Mohammed, Raphael Babatunde Adeniyi
Journal of Advances in Mathematics and Computer Science · pp. 41–52 · Published 17 Dec 2014
10.9734/BJMCS/2015/14769Abstract
In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBDF) for the solution of second order Initial Value Problems (IVPs). The method is derived by the interpolation and collocation of the assumed approximate solution. The single continuous formulation derived is evaluated at grid point of X = Xn+k and its second derivative at X = Xn+j, j = 1,2,.....k - 1 and X = Xn+μ respectively, where k is the step number of the methods. The interpolation and collocation procedures lead to a system of (k+1) equations, which are solved to determine the unknown coefficients. The resulting coefficients are used to construct the approximate continuous solution from which the Multiple Finite Difference Methods (MFDMs) are obtained and simultaneously applied to provide the direct solution to IVPs. Numerical examples are given to show the efficiency of the method.
Cited by 2
U. Mohammed, R. Adeniyi, M. Semenov · 2018
Ibrahim Ahmed, A. I. Ma’Ali, A. A. Agboluaje · FUDMA JOURNAL OF SCIENCES · 2025
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