|
Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, : The ''parameter'' is usually a real scalar, and the ''solution'' an ''n''-vector. For a fixed ''parameter value'' , maps Euclidean n-space into itself. Often the original mapping 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 . == Other forms == In some nonlinear systems, parameters are explicit. In others they are implicit, and the system of nonlinear equations is written : where is an ''n''-vector, and its image is an ''n-1'' vector. This formulation, without an explicit parameter space is not usually suitable for the formulations in the following sections, because they refer to parameterized autonomous nonlinear dynamical systems of the form: : However, in an algebraic system there is no distinction between unknowns and the parameters. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「numerical continuation」の詳細全文を読む スポンサード リンク
|