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2. THE POWER SERIES APPROXIMATION OF THE THIRD DERIVATIVE BLOCK METHOD FOR THE SOLUTION OF HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS by 1J. Sabo, 2F. J. Adeyeye and 3Y. Skwame 1,3 pp11 – 16 Volume 61
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Journal of the Nigerian Association of Mathematical Physics

Volume 61 (July – September 2021 Issue), pp11 – 16

© J. of NAMP

THE POWER SERIES APPROXIMATION OF THE THIRD DERIVATIVE BLOCK

METHOD FOR THE SOLUTION OF HIGHER ORDER ORDINARY DIFFERENTIAL

EQUATIONS

1J. Sabo, 2F. J. Adeyeye and 3Y. Skwame

1,3 

Department of Mathematical sciences, Adamawa State University, Mubi, Nigeria

2Department of Math/Computer science, Federal University of Petroleum Resource, Effurum, Nigeria.

Abstract

In this research, we propose a approximation of third derivative for the direct  solution of higher order ODEs. The method was derived via interpolation and collocation by the introduction of off-mesh point at both grid and off-grid, using the power series. The analysis of the method was examined, and it was found to be consistent, zero-stable, convergent and absolutely stable. The method was tested on three highly stiff problems and from the results obtained, the method are more accurate than the existing methods. We further sketched the solution graph of this method and it is evident that the new method convergence toward the exact solution.

Keyword: Third derivative, ODEs, Interpolation and collocation, Off-mesh point, Power series, Highly stiff problem.

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