Abstract
Algorithms and comparison results for a derivative-free predictor-corrector method for following arcs of H(x,t) = ϑ, where H : Rn × [0, 1] → Rn is smooth, are given. The method uses a least-change secant update for H', adaptive controlled predictor stepsize, and Powell's indexing procedure to preserve linear independence in the updates. Considerable savings in numbers of theoretical function calls are observed over high order methods requiring explicit H'. The framework of a promising technique for handling general bifurcation problems is presented.
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© 1981 Springer-Verlag
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Kearfott, R.B. (1981). A derivative-free arc continuation method and a bifurcation technique. In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090682
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DOI: https://doi.org/10.1007/BFb0090682
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