Computing Evans functions numerically via boundary-value problems
Numerical Analysis
2018-01-17 v1
Abstract
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.
Cite
@article{arxiv.1710.02500,
title = {Computing Evans functions numerically via boundary-value problems},
author = {Blake Barker and Rose Nguyen and Björn Sandstone and Nathan Ventura and Colin Wahl},
journal= {arXiv preprint arXiv:1710.02500},
year = {2018}
}
Comments
17 pages, 7 figures