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A Bisection-Like Algorithm for Branch Switching at a Simple Branch Point

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Abstract

At a Simple Branch Point x 0 of a parameter-dependent nonlinear system, two distinct solutions branches S 1 and S 2 intersect. A popular method of branch switching from S 1 to S 2 at x 0 is to use an orthogonal vector to the tangent vector to S 1 at x 0 as an initial guess for the tangent vector to S 2 at x 0. We describe an improved version of this method using a bisection-like procedure, which is especially useful for large problems.

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Authors and Affiliations

  1. Mathematical Sciences Department, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    J. Hughes & M. Friedman

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  1. J. Hughes
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  2. M. Friedman
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Correspondence to M. Friedman.

Additional information

J. Hughes and M. Friedman were supported in part under NSF DMS-0209536 and NSF ATM-0417774.

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Hughes, J., Friedman, M. A Bisection-Like Algorithm for Branch Switching at a Simple Branch Point. J Sci Comput 41, 62–69 (2009). https://doi.org/10.1007/s10915-009-9306-0

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  • DOI: https://doi.org/10.1007/s10915-009-9306-0

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