Abstract
Up to now we have been discussing ways of numerically tracing a curve ℌ ⊂ H−1(0) where H : RN+1 → RN. We have outlined both the predictor-corrector methods which rest rather strongly upon smoothness properties of H and the piecewise-linear methods which require less smoothness, but then on the other hand are generally less flexible as far as allowing general step-lengths is concerned. The latter methods are also no longer viable for large N. The behavior of the two methods was also seen to be considerably different in the presence of singular points on the curve.
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© 1990 Springer-Verlag Berlin Heidelberg
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Allower, E.L., Georg, K. (1990). Approximating Implicitly Defined Manifolds. In: Numerical Continuation Methods. Springer Series in Computational Mathematics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61257-2_15
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DOI: https://doi.org/10.1007/978-3-642-61257-2_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64764-2
Online ISBN: 978-3-642-61257-2
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