Academic Journal of Applied Mathematical Sciences
Online ISSN: 2415-2188
Print ISSN: 2415-5225
Print ISSN: 2415-5225
Quarterly Published (4 Issues Per Year)
Archives
Volume 3 Number 4 April 2017
Two-Step Block Hybrid Multistep Method for the Solution of (Equation in Pdf)
Authors: Abada A. A. ; Aboiyar T. ; Awari Y. S.
Pages: 40-45
Abstract
This paper proposes a self-starting block hybrid method of order 
for the solution of general second order ODEs of the form 
, 
with associated initial or boundary conditions. Derivation of the continuous hybrid formulation was based on the use of hermite polynomial as basis function. The continuous hybrid formulation enables us to evaluate and then differentiate at some grid and off-grid points to obtained discrete schemes which were used in block form. This approach eliminates the need for starting values. The computational burden and computer time wastage involved in the usual reduction of the second order problem into system of first order equations are avoided by this procedure. The stability properties of our method reveal that the method is consistent and zero stable, hence convergent. Numerical results suggest that the method performs favorably with the existing methods.
for the solution of general second order ODEs of the form , with associated initial or boundary conditions. Derivation of the continuous hybrid formulation was based on the use of hermite polynomial as basis function. The continuous hybrid formulation enables us to evaluate and then differentiate at some grid and off-grid points to obtained discrete schemes which were used in block form. This approach eliminates the need for starting values. The computational burden and computer time wastage involved in the usual reduction of the second order problem into system of first order equations are avoided by this procedure. The stability properties of our method reveal that the method is consistent and zero stable, hence convergent. Numerical results suggest that the method performs favorably with the existing methods. 
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