A Two Dimensional Continuation Solver Using Software Layering

One-dimensional continuation techniques, which are well-established, compute the solution curve to a non-linear system of n equations in n+1 unknowns. Typically, the "extra" unknown is interpreted as a free parameter to be varied over some interval. The solution curve, then, represents the behavior of the equations with respect to this parameter. As a practical example, imagine studying the behavior of a non-linear electronic network as temperature is varied from 0 to 125 degrees.