The resulting linear equation was solved for using a banded solver.
The threshold value c = 4 is the speed of propagation for solutions of the linear equation with spatially localized initial conditions.
The linear equation that best expressed this relationship across all vessels in the sample was then solved for using regression analysis.
The simplest model is that of a perturbed linear equation with parameters (the perturbation is nonlinear).
We therefore use a linear equation of state for surface tension.
Unknown to them, the parameters of the system are governed by a linear equation.
There are two reasons why $, determined from the linear equation (?), takes non-zero values below this line.
Perturbation methods are applied to the basic equations of flow to obtain a linear equation governing the stream function of the perturbation.