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Numerical Taylor expansions for invariant manifolds

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Summary.

We consider numerical computation of Taylor expansions of invariant manifolds around equilibria of maps and flows. These expansions are obtained by writing the corresponding functional equation in a number of points, setting up a nonlinear system of equations and solving this system using a simplified Newton’s method. This approach will avoid symbolic or explicit numerical differentiation. The linear algebra issues of solving the resulting Sylvester equations are studied in detail.

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, 1100, 02015, Hut, Finland

    Timo Eirola & Jan von Pfaler

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  1. Timo Eirola
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  2. Jan von Pfaler
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Correspondence to Timo Eirola.

Additional information

Mathematics Subject Classification (1991): 65Q05, 65P, 37M, 65P30, 65F20, 15A69

Dedicated to Gerhard Wanner on the occasion of his 60’th birthday

Acknowledgments. The authors like to thank Olavi Nevanlinna for discussions and his suggestion to use complex evaluation points.

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Eirola, T., von Pfaler, J. Numerical Taylor expansions for invariant manifolds. Numer. Math. 99, 25–46 (2004). https://doi.org/10.1007/s00211-004-0537-6

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  • DOI: https://doi.org/10.1007/s00211-004-0537-6

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