This equation is integrated numerically, and the interchange instability growth rate is obtained as a function of the wave number.
Then, this equation is integrated over a control volume (mathcal{V}) (enclosed by a surface (mathcal {S})), extending from ((j-frac{1}{2})Delta z) to ((j+frac {1}{2})Delta z).
This equation is integrated and by fitting the calculated values of x1 to the data for x1, the parameters par are found.
This equation is numerically integrated using an adaptive Runge Kutta Fehlberg method, yielding the frequency- and spatially-dependent impedance matrix of the beam, from which the reflection matrix is obtained.
This equation has been integrated under non-isothermal conditions and assuming an Arrhenian temperature dependence of the nucleation frequency and of the crystal growth rate, thus obtaining a general expression for the volume fraction crystallized for each value of the related parameter with the dimensionality of the crystal.
This equation was numerically integrated using Mathematica Version 9, keeping in mind that [ N ] T and [ P] are time-dependent, to determine the total amount of dephosphorylation.
The model, constructed as a system of ordinary differential equations, integrates dynamics at two levels (pathogen competition at the individual level as immunological memory accumulates, and pathogen transmission at the population level) in a form that is inevitably dense.
Case 2. g ( u ) = u 2 2. Using the wave variable ξ = x − V t, then by integrating this equation and considering the constant of integration to be zero, we obtain ( V − β ) U − V U ′ ′ + α U ′ + 1 2 U 2 = 0. (25).
Integrating this equation and considering the constant of integration to be zero, we obtain ( − V + α ) U + V U ′ ′ + β U 2 + θ U 3 − γ − 1 2 ( U ′ ) 2 − U U ′ ′ = 0. (39).
Using the wave variable ξ = x − V t in (19) then integrating this equation and considering the constant of integration to be zero, we obtain ( − V + γ ) U − α U ′ + θ 2 U 2 + ( V + β ) U ′ ′ = 0. (20..
