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Two-Step Block Hybrid Multistep Method for the Solution of (Equation in Pdf)

Abada A. A., Aboiyar T. and Awari Y. S.
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Abada A. A.: Department of Mathematical Sciences, Taraba State University, Jalingo. Nigeria
Aboiyar T.: Department of Mathematics/Stat./Computer Science, Federal University of Agriculture, Makurdi, Nigeria
Awari Y. S.: Department of Mathematics/Statistics, Bingham University, Karu, Nigeria

Academic Journal of Applied Mathematical Sciences, 2017, vol. 3, issue 4, 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.Â

Keywords: Block method; Hermite polynomial; Interpolation and collocation; Basis function; Second order ODEs. (search for similar items in EconPapers)
Date: 2017
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