perturbation theory

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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 ?
These proposed homotopy perturbation methods are applied and figures present solutions are presented using different values for the derivative order [alpha].
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.
Liu, "Application of homotopy perturbation methods for solving systems of linear equations," Applied Mathematics and Computation, vol.
In the 70s and 80s, ID perturbation methods were developed; they removed thin layers of material from the suction and pressure sides of the airfoil.
HAM, as an analytical method, has an advantage over perturbation methods in that it does not depend on small or large parameters.
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.