Sentence examples for using the asymptotic solutions from inspiring English sources

We are describing the stable nonautonomous planar dynamic systems with complex coefficients by using the asymptotic solutions (phase functions) of the characteristic (Riccati) equation.

Using the asymptotic solutions of the convection diffusion equation, we develop new correlations for mass transfer coefficients for the case of developing laminar flow that agree with numerical solutions of the Navier Stokes equations, and theory in the limits.

For the uniformly wetted geometry, because of the relative simplicity of the boundary conditions, the approximate model using the asymptotic solutions at small and large Thiele moduli derived in a similar way as for the polar wetted case provides satisfactory results.

A quantitative measure of the effectiveness of the reaction is derived using the asymptotic downstream solution.

At the end of this section, for the sake of comparison, we recall the main results of [8, 17], where summation characterizations of recessive solutions of (1.1) are investigated using the asymptotic analysis of the solution space of (1.1).

These points include mapping the domain of the ODE into a finite one, using the asymptotic form of the solutions, best use of the normalization freedom, and converting the δ-functions into boundary conditions.

Solutions of nonlinear smooth PDE problems may be approximated as higher order truncated Taylor series using the Asymptotic Numerical Method (ANM).

The homogenization procedure is justified using the asymptotic expansion method.

b Using the asymptotic standard error assuming the null hypothesis.

Hardy Weinberg equilibrium was tested using the asymptotic Pearson's χ-test.

For the thermocapillary motion of two-droplet systems, our results for the droplet interaction parameters agree very well with the exact solutions obtained by using spherical bipolar coordinates or the asymptotic solutions obtained by using a method of reflections.