1 Answers
Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations,
The parameter λ {\displaystyle \lambda } is usually a real scalar, and the solution u {\displaystyle \mathbf {u} } an n-vector. For a fixed parameter value λ {\displaystyle \lambda } , F {\displaystyle F} maps Euclidean n-space into itself.
Often the original mapping F {\displaystyle F} is from a Banach space into itself, and the Euclidean n-space is a finite-dimensional Banach space.
A steady state, or fixed point, of a parameterized family of flows or maps are of this form, and by discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of F = 0 {\displaystyle F=0}.