Abdelrahim, Ra’ft and Omar, Zurni (2017) A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly. Journal of King Saud University - Science, 29. pp. 401-412. ISSN 10183647

PDF Restricted to Registered users only Download (604kB) | Request a copy

Abstract

The existing hybrid methods for solving ordinary differential equations were only derived using specific off-step points. Thus, this paper proposes a new four-step block method with three generalized off-step points for solving initial value problems of fourth order ordinary differential equations directly. The strategy employed to develop this method is interpolating the basis function at ynþj; j ¼ 0ð1Þ3 and collocating the fourth derivative of the basis function at all points within the selected interval. The implementation of this method in a block-by-block fashion can overcome the setbacks of applying starting values and predictors which are created in predictor-corrector approach. The convergence analysis of the developed method is performed and the accuracy of the method is tested on several problems. The numerical results indicate that the new method outperforms the existing ones in terms of errors. In addition, the new method does not require much computation when compared with previous methods.

Item Type:	Article
Uncontrolled Keywords:	Block method, Hybrid block method, Fourth order ordinary differential equations, Collocation and interpolation, Three off-step points
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions:	School of Quantitative Sciences
Depositing User:	Mrs. Norazmilah Yaakub
Date Deposited:	06 Dec 2020 06:42
Last Modified:	06 Dec 2020 06:42
URI:	https://repo.uum.edu.my/id/eprint/27951

Actions (login required)

View Item