A new algorithm for two-dimensional numerical continuation

Consider a smooth mapping F from n+2 into n; such a mapping can be interpreted as a system of n functions in n + 2 unknowns. The zero-set of the mapping is typically a smooth two-dimensional manifold (surface) embedded in the ambient space of dimension n + 2. Our paper describes a numerical algorithm for generating a representation of such a surface which can be displayed graphically. The defining equations are given in implicit form; not only is such a formulation convenient, but it allows surfaces with “folds” in which there is not a functional relationship between the n state space variables and the two distinguished continuation parameters. The algorithm is built as a layer on top of an existing one-dimensional continuation solver, and has been successfully applied to problems with a high-dimensional state space using efficient sparse matrix techniques. Appli ations in electronic circuit simulation are described.