Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
High order Runge-Kutta methods on manifolds
proceedings of the on Numerical analysis of hamiltonian differential equations
On manifolds of connecting orbits in discretizations of dynamical systems
Nonlinear Analysis: Theory, Methods & Applications
Error estimates for approximating non-hyperbolic heteroclinic orbits of maps
Numerische Mathematik
Transversal connecting orbits from shadowing
Numerische Mathematik
| Hi-index | 0.00 |
In this paper we propose a numerical method for approximating connecting orbits on a manifold and its bifurcation parameters. First we extend the standard nondegeneracy condition to the connecting orbits on a manifold. Then we construct a well-posed system such that the nondegenerate connecting orbit pair on a manifold is its regular solution. We use a difference method to discretize the ODE part in this well-posed system and we find that the numerical solutions still remain on the same manifold. We also set up a modified projection boundary condition to truncate connecting orbits on a manifold onto a finite interval. Then we prove the existence of truncated approximate connecting orbit pairs and derive error estimates. Finally, we carry out some numerical experiments to illustrate the theoretical estimates.