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Two point block multistep methods with trigonometric−fitting for solving oscillatory problems


Mansor, Aini Fadhlina and Ismail, Fudziah and Senu, Norazak (2019) Two point block multistep methods with trigonometric−fitting for solving oscillatory problems. Pertanika Journal of Science & Technology, 27 (4). pp. 2381-2398. ISSN 0128-7680; ESSN: 2231-8526


In this paper, we present the absolute stability of the existing 2-point implicit block multistep step methods of step number k = 3 and k = 5 and solving special second order ordinary differential equations (ODEs). The methods are then trigonometrically fitted so that they are suitable for solving highly oscillatory problems arising from the special second order ODEs. Their explicit counterparts are also trigonometrically fitted so that in the implementation the methods can act as a predictor-corrector pairs. The numerical results based on the integration over a large interval are given to show the performance of the proposed methods. From the numerical results we can conclude that the new trigonometrically-fitted methods are superior in terms of accuracy and execution time, compared to the existing methods in the scientific literature when used for solving problems which are oscillatory in nature.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Universiti Putra Malaysia Press
Keywords: Block method; Multistep method; Oscillatory problems; Special second order ODEs; Trigonometrically fitted
Depositing User: Nabilah Mustapa
Date Deposited: 04 Feb 2020 03:58
Last Modified: 04 Feb 2020 03:58
URI: http://psasir.upm.edu.my/id/eprint/76347
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