Numerical continuation

Summary

Numerical continuation is a family of methods that trace the solutions of a system of equations $F(x, \lambda) = 0$ as a parameter $\lambda$ changes. Starting from one known solution, it computes a chain of nearby solutions along a curve. Each new point usually comes from a predictor step and a Newton's method corrector step. It is the main tool for studying how the solutions of nonlinear models depend on parameters, and for finding bifurcations. It also gives a way to solve a hard system by deforming it from an easy one.