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TW 288
Z. Zheng and D.Roose
Computation of Homoclinic Bifurcations of PDEs Using a Multiple Shooting Newton-Picard Method
Abstract
Periodic solutions of large scale ODE systems, resulting from space discretization of a PDE system, can be computed efficiently using a shooting method, in which the nonlinear system is solved by a Newton-Picard iteration. For strongly unstable periodic solutions, a multiple shooting approach is necessary. This is for example the case for a periodic solution, approaching a homoclinic orbit, for which some of the Floquet multipliers tend to infinity. In this paper, we describe how a multiple shooting Newton-Picard method can be used to compute homoclinic bifurcations by solving a periodic boundary value problem. This is illustrated with results for a homoclinic bifurcation in the Kuramoto-Sivashinsky Equation.
report.pdf / mailto: D. Roose