perturbation theory

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perturbation theory

[‚pər·tər′bā·shən ‚thē·ə·rē]
(mathematics)
The study of the solutions of differential and partial differential equations from the viewpoint of perturbation of solutions.
(physics)
The theory of obtaining approximate solutions to the equations of motion of a physical system when these equations differ by a small amount from equations which can be solved exactly.
References in periodicals archive ?
Various perturbation methods [1, 2] have been widely applied for obtaining approximate solutions of these equations, involving small parameter.
In the present work, we extend a homotopy perturbation method with time-fractional derivatives to obtain solution for oxygen diffusion problem.
Here, we use alternative approach to solve (2) based on homotopy perturbation method (HPM).
Perturbation method provides an expression for the desired solution in terms of a formal power series in a parameter that quantifies the deviation from the exactly solvable problem.
Application of iteration perturbation method for nonlinear oscillators with discontinuities, Int.
Example include Yldrm and Momani [18] who applied the homotopy perturbation method (HPM) to fractional oscillator and Koak and Yldrm [19] who solved the 3D Green's function by using HPM.
An additional advantage of higher-order perturbation methods is that, like their first-order counterparts, they do not suffer from the curse of dimensionality.
An introduction on analysis, modeling, coupling methods and perturbation methods is included.
Standard perturbation methods provide a Taylor expansion of the policy functions that characterize the equilibrium of the economy in terms of the state variables of the model and a perturbation parameter.
While perturbation methods guarantee that complete or exact disclosure (i.
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.