Simple algorithms for tracing solution curves

The author presents some simple and practical algorithms for tracing implicitly defined solution curves. These algorithms use hyperspheres instead of hyperplanes that are used in the typical predictor-corrector algorithms. Effective techniques for preventing the reversion phenomenon of the curve tracing are also proposed. The proposed algorithms are geometrically clear and can be easily programmed. It is also shown that the algorithms can be easily implemented on existing circuit simulators such as SPICE.<>