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Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae


Citation

Asnor, Asma Izzati and Mohd Yatim, Siti Ainor and Ibrahim, Zarina Bibi (2019) Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae. Symmetry, 11 (10). art. no. 1289. pp. 1-10. ISSN 2073-8994

Abstract

Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the selection of the least computed LTE among the three orders of VOHOBBDF and switch the code to the method that produces the least LTE for the next step. A few numerical experiments on the focused problem were performed to investigate the numerical efficiency of implementing VOHOBBDF methods in a single code. The analysis of the experimental results reveals the numerical efficiency of this approach as it yielded better performances with less computational effort when compared with built-in stiff Matlab codes. The superior performances demonstrated by the application of adaptive orders selection in a single code thus indicate its reliability as a direct solver for higher order stiff ODEs.


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Official URL or Download Paper: https://www.mdpi.com/2073-8994/11/10/1289

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.3390/sym11101289
Publisher: MDPI
Keywords: Block backward differentiation formula; Stiff ordinary differential equations; Third order ordinary differential equations; Variable order
Depositing User: Nabilah Mustapa
Date Deposited: 04 May 2020 16:04
Last Modified: 04 May 2020 16:04
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/sym11101289
URI: http://psasir.upm.edu.my/id/eprint/38236
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