Numerical continuation

Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, 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 ( ∗ , λ ) {displaystyle F(ast ,lambda )} 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 approximation to the 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} .