Comparison of approximate symmetry methods for differential equations
type: Item
instance of: scholarly article
title: Comparison of approximate symmetry methods for differential equations
zbMATH Open document ID: 1066.76052
DOI: 10.1023/B:ACAP.0000018792.87732.25
published in: Acta Applicandae Mathematicae
publication date: 2005-01-17T00:00:00Z
review text: Exact and approximate symmetries of potential Burgers equation are calculated by the usage of two known approximate symmetry methods [\textit{V. A. Bajkov, R. K. Gazizov} and \textit{N. Kh. Ibragimov}, Math. USSR, Sb. 64, No.~2, 427--441 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No.~4(8), 435--450 (1988; Zbl 0683.35004); \textit{W. I. Fushchich} and \textit{W. H. Shtelen}, J. Phys A, Math. Gen. 22, 887--890 (1989)] and their modifications. Comparisons are made between those two methods and the exact symmetries of the equation. Approximate solutions corresponding to the approximate symmetries are derived for each case and compared. The non-Newtonian creeping flow equations of a second-grade fluid is considered, and approximate symmetries are computed by different methods together with approximate solutions for each method and their comparisons. Finally, a singular perturbation problem is investigated.
Mathematics Subject Classification ID: 76M60
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 2128506
zbMATH Keywords: Lie group method
author: Mehmet Pakdemirli
author: Muhammet Yürüsoy
author: İhsan Timuçin Dolapçı
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
Wikidata QID: Q58206734
full work available at URL: b:acap.0000018792.87732.25
OpenAlex ID: W2008884333
description: scientific article; zbMATH DE number 2128506