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Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations


Citation

Jana Aksah, Saufianim and Ibrahim, Zarina Bibi and Mohd Zawawi, Iskandar Shah (2019) Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations. Mathematics, 7 (2). art. no. 211. pp. 1-16. ISSN 2227-7390

Abstract

In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation of the Jacobian and one LU decomposition for each time step. For the SDIBBDF method to have practical significance in solving stiff problems, its stability region must at least cover almost the whole of the negative half plane. Step size restriction of the proposed method have to be considered in order to ensure stability of the method in computing numerical results. Efficiency of the SDIBBDF method in solving stiff ODEs is justified when it managed to outperform the existing methods for both accuracy and computational time.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.3390/math7020211
Publisher: MDPI
Keywords: Singly diagonally implicit; Block multistep method; A-stable; Step-size restriction; Stiff ODEs
Depositing User: Nabilah Mustapa
Date Deposited: 04 May 2020 16:58
Last Modified: 04 May 2020 16:58
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/math7020211
URI: http://psasir.upm.edu.my/id/eprint/77850
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