perturbation theory

(redirected from Perturbation methods)
Also found in: Encyclopedia.

perturbation theory

n.
A set of mathematical methods often used to obtain approximate solutions to equations for which no exact solution is possible, feasible, or known.
References in periodicals archive ?
This allows the systematic use of perturbation methods.
Liao edits this research volume on applications of the homotopy analysis method (HAM) in nonlinear problems, particularly where other common approaches such as perturbation methods may not be appropriate.
17) When recursive equilibria fail to exist, the perturbation methods used in the literature and this paper cannot be applied (see Peralta-Alva and Santos.
In particular oscillators with fractional-power nonlinearities have been the subject of active research in recent years which have proposed to analyze them by, besides numerical techniques, approximate methods such as perturbation methods, harmonic balance, slowly varying amplitude and phase and so on [9-25].
Nine appendices (about 40 pages) give background on mathematical relations, gamma and beta functions, Fourier series, basic theorems of the theory of second-order and linear second-order differential equations, perturbation methods, and discrete models of two TNL oscillations.
The principal conclusion is that the perturbation methods are most applicable to RTO problems where there are few degrees of freedom (independent manipulated variables) for optimization and process measurement noise is not a significant factor.
An additional advantage of higher-order perturbation methods is that, like their first-order counterparts, they do not suffer from the curse of dimensionality.
The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering.
Fixed-data perturbation methods usually generate an entirely new database, for secondary use.
For most examples, he shows how the result is equivalent to results from other perturbation methods such as the methods of multiple scales and averaging.
These expressions are valid for a wide range of vibration amplitudes, unlike the solutions obtained by the other analytical techniques such as perturbation methods.