IJPAM: Volume 103, No. 3 (2015)

BLOCK METHOD WITH ONE HYBRID POINT FOR
THE SOLUTION OF FIRST ORDER INITIAL VALUE
PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

A.U. Fotta$^1$, T.J. Alabi$^2$, B. Abdulqadir$^3$
$^{1}$Department of Mathematics
Adamawa State Polytechnic
Yola, Adamawa State, NIGERIA
$^{2}$Department of Mathematics/Statistics
Kogi State Polytechnic
Lokoja, NIGERIA
$^{3}$Department of Mathematics
Federal College of Education
Yola, Adamawa State, NIGERIA


Abstract. This paper discussed the development of one - step, one hybrid block method for the solution of first order initial value problems. Two functions were combined to form the basis function which is collocated and interpolated at some selected grid and off-grid points to develop a linear multistep method which is implemented in block form. The paper further investigated the properties of the block method and found it to be convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to give better approximation than the methods we compared our results with.

Received: May 8, 2015

AMS Subject Classification: 65L05, 65L06, 65D30

Key Words and Phrases: hybrid, consistent, grid points, off-grid points, convergent, block method, exponential function, interpolation

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DOI: 10.12732/ijpam.v103i3.12 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: 2015
Volume: 103
Issue: 3
Pages: 511 -


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