Multiple-scale analysis: Difference between revisions

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In [[mathematics]] and [[physics]], '''multiple-scale analysis''' (also called the '''method of multiple scales''') refers to techniques used to construct uniformly valid [[approximation]]s to the solutions of [[perturbation theory|perturbation problems]], both for small as well as large values of the [[independent variable]]s. This is done by introducing fast-scale and slow-scale variable(s) for an independent variable, and subsequently treating these variables, fast and slow, as if they are independent. In the solution process of the perturbation problem thereafter, the resulting additional freedom – introduced by the new independent variables – is used to remove (unwanted) [[secular variation|secular terms]]. ThisThe latter puts constraints on the approximate solution, which constraints are called '''solvability conditions'''.

==Example: undamped Duffing equation==