A Hermite spectral method for the computation of homoclinic orbits and associated functionals

Authors:
Valeriy R. Korostyshevskiy;Thomas Wanner
Affiliations:
Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University Medical Center, Washington, DC 20057, USA;Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 11
Cited 0

Numerical computation of heteroclinic orbits

Journal of Computational and Applied Mathematics - Continuation Techniques and Bifurcation Problems
A fourier-series method for solving soliton problems

SIAM Journal on Scientific and Statistical Computing
Numerical computation and continuation of invariant manifolds connecting fixed points

SIAM Journal on Numerical Analysis
The Hermite spectral method for Gaussian-type functions

SIAM Journal on Scientific Computing
The dynamics of nucleation for the Cahn-Hilliard equation

SIAM Journal on Applied Mathematics
The numerical computation of connecting orbits in dynamical systems: a rational spectral approach

Journal of Computational Physics
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics

Proceedings of the workshop on Time-reversal symmetry in dynamical systems
A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem

SIAM Journal on Numerical Analysis
Slow motion in higher-order systems and &Ggr;-convergence in one space dimension

Nonlinear Analysis: Theory, Methods & Applications
Laguerre approximation of stable manifolds with application to connecting orbits

Mathematics of Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Quantified Score

Hi-index	7.29

Visualization

Abstract

We present a spectral method for the computation of homoclinic orbits in ordinary differential equations. The method is based on Hermite-Fourier expansions of the complete homoclinic solution and exhibits exponential convergence. In addition, our method can be used to approximate nonlinear functionals which depend on the complete homoclinic solution. This is demonstrated using examples from phase separation dynamics and metastability.