ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65M12, 65M15, 35B32, 58F14
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. The long-time behaviour of numerical approximations to the solutions of a semilinear parabolic equation undergoing a Hopf bifurcation is studied in this paper. The framework includes reaction-diffusion and incompressible Navier-Stokes equations. It is shown that the phase portrait of a supercritical Hopf bifurcation is correctly represented by Runge-Kutta time discretization. In particular, the bifurcation point and the Hopf orbits are approximated with higher order. A basic tool in the analysis is the reduction of the dynamics to a two-dimensional center manifold. A large portion of the paper is therefore concerned with studying center manifolds of the discretization.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050384
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