Article ID: | iaor20126137 |
Volume: | 61 |
Issue: | 3 |
Start Page Number: | 429 |
End Page Number: | 464 |
Publication Date: | Nov 2012 |
Journal: | Numerical Algorithms |
Authors: | Liu Yuanyuan, Zou Yongkui |
Keywords: | algebra |
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.