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Zbl 1066.76052
Pakdemirli, M.; Yürüsoy, M.; Dolapçi, İ.T.
Comparison of approximate symmetry methods for differential equations. (English)
[J] Acta Appl. Math. 80, No. 3, 243-271 (2004). ISSN 0167-8019; ISSN 1572-9036/e

Exact and approximate symmetries of potential Burgers equation are calculated by the usage of two known approximate symmetry methods [{\it V. A. Bajkov, R. K. Gazizov} and {\it 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); {\it W. I. Fushchich} and {\it 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.
[Boris V. Loginov (Ul'yanovsk)]

MSC 2000:: *76M60 Symmetry analysis, Lie group and algebra methods
76A05 Non-Newtonian fluids
35Q35 Other equations arising in fluid mechanics
35A30 Geometric theory for PDE, transformations

Keywords: Lie group method;

Citations: Zbl 0683.35004

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