eprintid: 18770
rev_number: 2
eprint_status: archive
userid: 1
dir: disk0/00/01/87/70
datestamp: 2024-06-04 14:11:10
lastmod: 2024-06-04 14:11:10
status_changed: 2024-06-04 14:04:02
type: article
metadata_visibility: show
creators_name: Zainuddin, N.
creators_name: Ibrahim, Z.B.
creators_name: Zawawi, I.S.M.
title: Diagonal Block Method for Stiff Van der Pol Equation
ispublished: pub
keywords: Iterative methods, BDF; Block methods; Computational costs; Pol equation; Step size; Stiff; Stiff equations; Time components; Van der Pol; Van der pol equation, Numerical methods
note: cited By 1
abstract: Stiff equation is known for its rapid and slow varying time component, for which the method dedicated for this system must be capable on changing the step size depending on the varying component of the interval. This is to make sure that the computational cost can be reduced while the accuracy is preserved. In this paper, the diagonal block method derived from the family of backward differentiation formula is proposed for the direct solution of stiff Van der Pol equation. The method is implemented by varying the step size in the fixed ratios of 1, 2 and 10/19 which corresponds to constant, by halving and increasing the step respectively. The method is derived in block forms to compute the approximate solutions at two points simultaneously. By controlling the constants in its linear difference operator, the consistency of the derived method is verified. The Newton iteration technique which is derived in the block matrix form is also presented in this paper. The robustness of the proposed method is validated by solving the stiff Van der Pol equation directly and compared with the ode15s from MATLAB. Numerical results demonstrate the capability of the proposed method in solving the stiff ODEs directly. © 2023,IAENG International Journal of Computer Science. All Rights Reserved.
date: 2023
publisher: International Association of Engineers
official_url: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149665069&partnerID=40&md5=a4f9e686ccee84096c558b9dba35bae5
full_text_status: none
publication: IAENG International Journal of Applied Mathematics
volume: 53
number: 1
refereed: TRUE
issn: 19929978
citation:   Zainuddin, N. and Ibrahim, Z.B. and Zawawi, I.S.M.  (2023) Diagonal Block Method for Stiff Van der Pol Equation.  IAENG International Journal of Applied Mathematics, 53 (1).   ISSN 19929978