Abstract
A numerical method for the direct computation of Hopf bifurcation points for a system of parabolic “diffusion-reaction” partial differential equations is described.A finite-difference discretization in space is used to approximate these equations by a system of first-order ordinary differential equations. The Hopf bifurcation of the latter system is computed by using Kubicek’s method. The results are improved by Richardson extrapolation. For approximation of the space operator, a standard three-point difference formula as well as the Stormer–Numerov technique are used. The method proposed is illustrated on an example describing heat and mass transfer in a porous catalyst particle.
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