By P. J. Aston, A. Spence, W. Wu (auth.), Dirk Roose, Bart De Dier, Alastair Spence (eds.)

ISBN-10: 9400906595

ISBN-13: 9789400906594

ISBN-10: 9401067813

ISBN-13: 9789401067812

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Additional info for Continuation and Bifurcations: Numerical Techniques and Applications

Example text

For the steady-state solutions discussed here, it is a trivial matter to recognise symmetries in a trigonometric expansion, but except for the simplest 2-fold symmetry this is not easy with a Chebyshev expansion or other techniques such as finite difference or finite element methods. Once symmetries have been recognised, of course, any method can be programmed to take advantage of a known symmetry, but again it is simpler to switch between calculations with different symmetries in the trigonometric representation.

B. Scheurer, R. Temam (1989), Some global dynamical propertiell of a clasll of pattern formation equations, Commun. in Partial Differential Equations, 14, pp. 245-297. Orszag, S. A. (1971), Numericaillimulation of incomprellilible flowil within lIimple boundaries: Accuracy, J. , 49, pp. 75-112. Orszag, S. A. (1972), Comparillon ofplleudollpectral and IIpectral approzimation, Studies in Appl. , 51, pp. 253-259. G. Kevrekidis, and B. Nicolaenko (1988), Scaling lawlI and the prediction of bifurcationll in lIylltemil modeling pattern formation, Phys.

4. 1322. This singularity is of topological co dimension 2 and is unfolded by p and t, its local behaviour around E is given by Fig. 4 in Golubitsky-Schaeffer ([15], pg 277). A similar analysis for the (1,2)-mode interaction, along the lines of [1], brings the following result. 0139. The singularity is completely unfolded by p and t and the normal form unfolding is given by -AZ - zy - az AY - z2 _ y2 + f3 y 3 o o (4) (5) 35 A c -------c , , .. -- -----~ , '" o ,; B ----~ E Figure 5: Codimension 2 diagrams where z, yare the 1, resp.

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Continuation and Bifurcations: Numerical Techniques and Applications by P. J. Aston, A. Spence, W. Wu (auth.), Dirk Roose, Bart De Dier, Alastair Spence (eds.)


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