TY - JOUR
T1 - The application of centre manifolds to amplitude expansions. I. Ordinary differential equations
AU - Carr, Jack
AU - Muncaster, Robert G.
N1 - Funding Information:
* Research completed during a visit to the Division of Applied Mathematics, Brown University, Providence, R. I., during 197881979, and was supported in part by the United States Army, Durham, under Grant ARODDAAG 29-76-G0294. ’ Research supported initially by a grant from the Science Research Council of Great Britain during a visit to Heriot-Watt University, Edinburgh, in 1976-1979, and subsequently by the National Science Foundation under Grant MCS-8001845.
PY - 1983/11
Y1 - 1983/11
N2 - The theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics.
AB - The theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics.
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U2 - 10.1016/0022-0396(83)90077-3
DO - 10.1016/0022-0396(83)90077-3
M3 - Article
AN - SCOPUS:0001226485
SN - 0022-0396
VL - 50
SP - 260
EP - 279
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -