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Journal of Scientific Research and  Studies

Journal of Scientific Research and Studies Vol. 5(1), pp. 15-20, January, 2018

ISSN 2375-8791

Copyright 2018

Author(s) retain the copyright of this article

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Full Length Research Paper

Error estimation of the differential Tau Method for certain fourth order boundary value problems

 

Yahaya Ajiya1*, Adamu Wakili2, Aliyu M. Awwal1, Aliyu Abubakar1 and Aminu Audu1

1Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria.
2Department of Mathematical Sciences, Faculty of Science, Federal University Lokoja, Kogi, Nigeria.
 

*Corresponding author. E-mail: ajiya2012@gmail.com Tel: +2348137811590

Accepted 31 December, 2017

 

 Abstract

 

In this paper, a generalized differential formulation of the Lanczos Tau Method and constructed polynomial error approximant of the error function for certain fourth order boundary value problems with first degree over-determination in ordinary differential equations were investigated; it is based on a modification of the error of Lanczos economization process. For this purpose, an algebraic linear system of equations was obtained by equating the corresponding coefficients of various powers of independent variable, in which these were solved to obtain the unknown constants. For the error estimation, two forms of homogeneous conditions of the error function were considered. Numerical experiments were given to illustrate the effectiveness of the method.

Key words: Chebyshev polynomial, differential operator, differential systems, error function, over-determination, Tau approximant, Tau parameter.

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