Numerical computation of heteroclinic orbits

摘要

We give a numerical method for the computation of heteroclinic orbits connecting two saddle points in R2. These can be computed to very high period due to an integral phase condition and an adaptive discretization. We can also compute entire branches (one-dimensional continua) of such orbits. The method can be extended to compute an invariant manifold that connects two fixed points in Rn. As an example we compute branches of traveling wave front solutions to the Huxley equation. Using weighted Sobolev spaces and the general theory of approximation of nonlinear problems we show that the errors in the approximate wave speed and in the approximate wave front decay exponentially with the period.