Computing Evans functions numerically via boundary-value problems
Autor: | Colin Wahl, Blake Barker, Rose Nguyen, Björn Sandstede, Nathaniel Ventura |
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Rok vydání: | 2017 |
Předmět: |
Partial differential equation
Computer science Computation Statistical and Nonlinear Physics Function (mathematics) Numerical Analysis (math.NA) Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Scheme (mathematics) 0103 physical sciences Scalability Convergence (routing) FOS: Mathematics Applied mathematics Boundary value problem Mathematics - Numerical Analysis 0101 mathematics Eigenvalues and eigenvectors |
DOI: | 10.48550/arxiv.1710.02500 |
Popis: | 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. Comment: 17 pages, 7 figures |
Databáze: | OpenAIRE |
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