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Branch switching in bifurcation problems for ordinary differential equations

  • The Uniform Stability of Singularly Perturbed Discrete and Continuous Boundary Value Problems
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Summary

The problem of switching branches in boundary-value problems of ordinary differential equations is considered. Three non-local methods for calculating emanating solutions near a nontrivial bifurcation point are proposed. These methods calculate one solution on an emanating branch (without a priori exact knowledge of the bifurcation point). Other solutions on the branch can be obtained by global continuation. The methods are convenient as they consist in solving boundary-value problems by standard software. The construction of an initial approximation of the emanating solution is outlined. A characteristic feature of the proposed methods is that they can be easily automated; the user can avoid nearly all preparatory work. The methods are tested on several examples arising in different application areas.

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  1. Mathematisches Institut der TU München, Postfach 202420, D-8000, München, (Fed. Rep.)

    R. Seydel

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  1. R. Seydel
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Seydel, R. Branch switching in bifurcation problems for ordinary differential equations. Numer. Math. 41, 93–116 (1983). https://doi.org/10.1007/BF01396308

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  • DOI: https://doi.org/10.1007/BF01396308

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