Sentence examples for using a power series from inspiring English sources

The differential equations are solved using a power series approach.

Mindlin's approach of using a power series expansion of the displacement field in the plate thickness coordinate was employed.

Using a power series expansion for the roots of the characteristic equation, the natural frequencies of a cantilevered Euler Bernoulli beam with an end rigid mass are computed.

A wave solution is used to describe the displacements of the cylindrical shell, while the displacements of the conical sections are solved using a power series solution.

In this paper, exact solutions for both the axisymmetric and antisymmetric modes of circular and annular membranes with any piecewise polynomial variation of the density are given using a power series solution.

where the integral can be calculated for most baseline distributions using a power series expansion for Q G (u).

To prove this result we use a power series expansion of the trace in terms of its conformal variations.

We use a power series of inverse Mill's ratio of the normalized estimated index.8 The semiparamteric estimator imposes a scale and location normalization for identification.

By using LAPM, a power series solution is essentially a truncated series solution.

Momoniat and Harley [16] obtained an approximate implicit solution by reducing the Lane-Emden equation to a first-order differential equation using Lie group analysis and determining a power series solution of the reduced equation.

The principle innovation is that, the present SBFEM model chooses Hankel function as a base solution for the unbounded sub-domain, while a power series is used for the internal bounded sub-domains.