Numerical methods for computing the Evans function

Abstract

This article presents the Lie midpoint method, the fourth order Magnus method and the Gauss--Legendre method for the numerical evaluation of the Evans function, a Wronskian-like determinant which arises in the study of the stability of pulse-type waves. Numerical examples and comparisons illustrate the three methods and their relative merits. The main advance is the ability to compute the Evans function for smaller step sizes. The efficiencies of the various methods are further illustrated by increasing the domain size.

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