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

Zumbrun, Kevin

doi:10.1090/S0033-569X-2010-01209-1

Author: Kevin Zumbrun
Journal: Quart. Appl. Math. 68 (2010), 557-561
MSC (2000): Primary 65L99
DOI: https://doi.org/10.1090/S0033-569X-2010-01209-1
Published electronically: May 27, 2010
MathSciNet review: 2676976
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Abstract: 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 surprisingly 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.

References

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