On the integration of stiff odes using block backward differentiation formulas of order six

Amiratul Ashikin Nasarudin; Zarina Bibi Ibrahim; Haliza Rosali

doi:10.3390/SYM12060952

On the integration of stiff odes using block backward differentiation formulas of order six

Amiratul Ashikin Nasarudin
, Zarina Bibi Ibrahim^*
, Haliza Rosali

^*Corresponding author for this work

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

277 Downloads (Pure)

Abstract

In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.

Original language	English
Article number	952
Journal	Symmetry
Volume	12
Issue number	6
DOIs	https://doi.org/10.3390/SYM12060952
Publication status	Published - 4 Jun 2020

Keywords

Block backward differentiation formula
Fully implicit
Off-step point

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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abstract = "In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.",

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AU - Nasarudin, Amiratul Ashikin

AU - Ibrahim, Zarina Bibi

AU - Rosali, Haliza

N1 - Funding Information: Funding: This research was funded by UNIVERSITI PUTRA MALAYSIA, under the Putra-IPS Grant (project no.:GP-IPS/2018/9624600). Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2020/6/4

Y1 - 2020/6/4

N2 - In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.

AB - In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.

KW - Block backward differentiation formula

KW - Fully implicit

KW - Off-step point

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ER -

On the integration of stiff odes using block backward differentiation formulas of order six

Abstract

Keywords

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