perturbation equation

perturbation equation

[‚pər·tər′bā·shən i‚kwā·zhən]
(physics)
Any equation governing the behavior of a perturbation; often this will be a linear differential equation.
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Equations (19)-(24) are highly ordered and nonlinear, so we use different techniques to calculate the 3-curvature perturbation equation. First, we will use [theta] + [psi] = [THETA] and find the solution of differential equation.
Here, [v.sub.t] = dF([bar.u])v is referred to as the linearization of (4) about [bar.u]; so, from this linearization, we obtain the linear perturbation equation.
The perturbation equation adopted in this study is the same as that used to perturb the global best particle solution in [17], where the global best particle is perturbed unconditionally.
which is a singular perturbation equation since the highest-order derivative has been multiplied by a small parameter, where 0 < [member of] = 1/[[mu].sup.2] [much less than] 1.
Now, we use their results to write the following perturbation equation corresponding to flat FRW universe which expands with acceleration.
Let us construct the homotopy perturbation equations
The zeroth-order perturbation equations describe a steady, zero-eccentricity flow condition and are listed below.
In the next section, we present the governing equations of motion and derive the associated perturbation equations. We introduce the linear and nonlinear analysis of our system in Section 3 and 4, respectively.
Following Ujevic and Letelier (2004), and for the sake of self-consistency of the current paper, in what follows we present the derivation (of the first-order perturbation equations for relativistic thin disks.
Abstract: I will describe in detail a package we developed recently that uses a fully geometrical method to derive perturbation equations about a spatially homogeneous background.
Based on the expansion (10), the perturbation equations could be obtained from (1)-(6) in the form:
The linearized perturbation equations are conveniently solved by a two-dimensional Fourier transform in the xy-plane and a Laplace transform in time, which result in ordinary differential equations in z for the transformed velocity and pressure perturbations, which can be solved analytically.