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Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly


Mansor, Kamarun Hizam and Omar, Zurni and Rohni, AM (2018) Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly. Journal of Advanced Research in Dynamical and Control Systems, 13 (SI). pp. 1-17. ISSN 1943-023X

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Abstract

This paper proposes a new two-step hybrid block method with one generalized off-step point within each step to find the direct solution of second order ordinary differential equation. In deriving this method, a power series is adopted as an approximate solution and interpolated at points while its second derivatives collocated at all points in the given interval to obtain the main continuous scheme. This method generates the non-overlapping starting values using Taylor series. The analysis of the method such as order, zero stability, consistency and convergence is also discussed. The developed method was then compared with the existing methods in terms of accuracy and the results suggest that this method can be served as a viable alternative methods to solve directly initial value problems of second order ordinary differential equations.

Item Type: Article
Additional Information: Abstract only
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: School of Quantitative Sciences
Depositing User: Mrs. Norazmilah Yaakub
Date Deposited: 02 Dec 2020 07:13
Last Modified: 02 Dec 2020 07:13
URI: http://repo.uum.edu.my/id/eprint/27942

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