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Mathematics 2019, 7(2), 211; https://doi.org/10.3390/math7020211

Stability Analysis of Singly Diagonally Implicit Block Backward Differentiation Formulas for Stiff Ordinary Differential Equations

1
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
2
Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
3
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Seremban Campus, 70300 Seremban, Negeri Sembilan, Malaysia
*
Author to whom correspondence should be addressed.
Received: 14 November 2018 / Revised: 27 January 2019 / Accepted: 28 January 2019 / Published: 25 February 2019
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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. View Full-Text
Keywords: singly diagonally implicit; block multistep method; A-stable; step-size restriction; stiff ODEs singly diagonally implicit; block multistep method; A-stable; step-size restriction; stiff ODEs
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Jana Aksah, S.; Ibrahim, Z.B.; Mohd Zawawi, I.S. Stability Analysis of Singly Diagonally Implicit Block Backward Differentiation Formulas for Stiff Ordinary Differential Equations. Mathematics 2019, 7, 211.

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