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Home  >  Volume 28. No.1 (Nov. 2014)

22. 3-Point Hybrid Block Method for the Numerical Integration of First Order Initial Value Problems by E. A. Areo - Volume28, No. 1, (November, 2014), pp 131 – 140
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Abstract 

In this paper, a multistep collocation technique isused to develop a 3-point hybrid block method for the numerical integration of Initial Value Problems (IVPs). 

The derivation of the block method is based on collocation of the differential system and the interpolation of the approximate solution at the grid and off-grid points. The approach is used to obtain Multiple Finite Difference Methods (MFDMs) which are 

combined as simultaneous numerical integrators to form the proposed block method. The individual schemes of the block method are investigated and found to be 

consistent, zero-stable and hence convergent. The proposed hybrid block method is tested on some standard IVPs to illustrate the accuracy and desirability of the new method.

 

Keywords:Hybrid block method, multistep, multiple finite difference, initial value problems, collocation, interpolation, consistent, zero-stable and convergent 

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