A local greedy algorithm and higher order extensions for global numerical continuation of analytically varying subspaces

Details A local greedy algorithm and higher order extensions for global numerical continuation of analytically varying subspaces A local greedy algorithm and higher order extensions for global numerical continuation of analytically varying subspaces

2008-09-28

arxiv.org/abs/0809.4725v2

Mathematics

Numerical Analysis

Added references plus discussuion of higher order algorithms

Scientific paper

We present a family of numerical implementations of Kato's ODE propagating global bases of analytically varying invariant subspaces, of which the first-order version is a surprising simple "greedy algorithm" that is both stable and easy to program and the second-order version a relaxation of a first-order scheme of Brin and Zumbrun. The method has application to numerical Evans function computations used to assess stability of traveling-wave solutions of time-evolutionary PDE.

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