IJPAM: Volume 83, No. 3 (2013)

CONTINUOUS BLOCK METHOD FOR THE SOLUTION OF
SECOND ORDER INITIAL VALUE PROBLEMS OF
ORDINARY DIFFERENTIAL EQUATION

A. Adewale James1, A. Olaide Adesanya2, Sunday Joshua3
1Mathematics Division
American University of Nigeria
Yola, Adamawa State, NIGERIA
2Department of Mathematics
ModibboAdama University of Technology
Yola, Adamawa State, NIGERIA
3Department of Mathematical Sciences
Adamawa State University
Mubi, Adamawa State, NIGERIA


Abstract. We proposed a continuous blocks method for the solution of second order initial value problems with constant step size in this paper. The method was developed by interpolation and collocation of power series approximate solution to generate a continuous linear multistep method;this is evaluated for the independent solution to give a continuous block method which is evaluated at selected grid point to give discrete block method. The basic properties of the method were investigated and was found to be zero stable, consistent and convergent. The efficiency of the method was tested on some numerical examples and found to give better approximation than the existing methods.

Received: September 24, 2012

AMS Subject Classification: 65205, 65L06, 65D30

Key Words and Phrases: collocation, continuous block method, interpolation, approximate solution

Download paper from here.



DOI: 10.12732/ijpam.v83i3.3 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 3