Two-Step Block Hybrid Multistep Method for the Solution of (Equation in Pdf)
Journal: Academic Journal of Applied Mathematical Sciences (Vol.3, No. 4)Publication Date: 2017-04-15
Authors : Abada A. A.; Aboiyar T.; Awari Y. S.;
Page : 40-45
Keywords : : Block method; Hermite polynomial; Interpolation and collocation; Basis function; Second order ODEs.;
- Two-Step Block Hybrid Multistep Method for the Solution of (Equation in Pdf)
- Three-Step Two-Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations
- APPLICATION OF TWO STEP CONTINUOUS HYBRID BUTCHER’S METHOD IN BLOCK FORM FOR THE SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEM
- An Implicit Two-Step One Off-Grid Point Third Derivative Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations
- A Class of One-Step Hybrid Third Derivative Block Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations
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.
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Last modified: 2018-11-03 14:13:31