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Padorean, J. and Tovichackhaikul, S. (1983) Operating Characteristics of Hyperbolically and Elliptically Constrained Self-Adaptive Incremental Newton-Raphson Algorithms. Journal Franklin Institute, 316, 197-223.
https://doi.org/10.1016/0016-0032(83)90041-8

has been cited by the following article:

• TITLE: Linear and Quadratic Leap-and-Land Trajectory Tracking Algorithms

  AUTHORS: Isaac Fried

  KEYWORDS: Implicit Functions, Curve Tracing, Linear Tangential Leap, Nonlinear Leaps, Maintaining Stability, Orthogonal Landing, Cornering a Snap-Through

  JOURNAL NAME: Applied Mathematics, Vol.12 No.7, July 14, 2021

  ABSTRACT: Considered in this note are numerical tracking algorithms for the accurate following of implicit curves. We start with a fixed point on the curve, and then systematically place on it additional points, one after the other. In this note we first go over the basic procedure of moving forward tangentially from an already placed point then orthogonally returning to the curve. Next, we further consider higher order forward stepping procedures for greater accuracy. We note, however, that higher order methods, desirable for greater accuracy, may harbor latent instabilities. This note suggests ways of holding such instabilities in check, to have stable and highly accurate tracing methods. The note has several supporting numerical examples, including the rounding of a dynamical “snap-through” point.