eprintid: 16419
rev_number: 2
eprint_status: archive
userid: 1
dir: disk0/00/01/64/19
datestamp: 2023-12-19 03:22:57
lastmod: 2023-12-19 03:22:57
status_changed: 2023-12-19 03:06:13
type: article
metadata_visibility: show
creators_name: Husin, N.M.
creators_name: Zawawi, I.S.M.
creators_name: Zainuddin, N.
creators_name: Ibrahim, Z.B.
title: Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler's Method
ispublished: pub
note: cited By 0
abstract: In this study, the fully implicit 2-point block backward differentiation formulas (BBDF) method has been successfully utilized for solving stiff ordinary differential equations (ODEs) by taking into account the uses of new starting methods namely, modified Euler�s method (MEM), improved modified Euler�s method (IMEM), and new Euler�s method (NEM). The reason of proposing the BBDF is that the method has been proven useful for stiff ODEs due to its A-stable properties. Furthermore, the method is able to approximate the solutions at two points simultaneously at each step. The proposed method is also implemented through Newton�s iteration procedure, which involves the calculation of the Jacobian matrix. Accuracy of the method is evaluated based on its performance in solving linear and non-linear initial value problems (IVPs) of first order stiff ODEs with transient and steady-state solutions. Some comparisons are made with the conventional BBDF approach for indicating the reliability of the proposed method. Numerical results indicate that not only classical Euler�s method provides accurate solutions for BBDF, but also the numerous modified versions of Euler�s methods improve the accuracy of BBDF, in terms of absolute error at certain step size and stage of iteration. © 2022 by authors. All rights reserved.
date: 2022
publisher: Horizon Research Publishing
official_url: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85137325686&doi=10.13189%2fms.2022.100506&partnerID=40&md5=939bda5f01480048ca87ee9df7a82a06
id_number: 10.13189/ms.2022.100506
full_text_status: none
publication: Mathematics and Statistics
volume: 10
number: 5
pagerange: 942-955
refereed: TRUE
issn: 23322071
citation:   Husin, N.M. and Zawawi, I.S.M. and Zainuddin, N. and Ibrahim, Z.B.  (2022) Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler's Method.  Mathematics and Statistics, 10 (5).  pp. 942-955.  ISSN 23322071