Sentence examples for by using numerical integration from inspiring English sources

The S-system is a formalism of ordinary non-linear differential equations, and thus the system can easily be solved numerically by using numerical integration algorithm customized specifically for this formalism [ 6].

Comparison of the results with those obtained by using numerical integration indicates the accuracy of the perturbation analysis.

In order to check the validity of the series expansions constructed, the domain of convergence corresponding to different orders is studied by using numerical integration.

A solution can be found by using numerical integration together with an algorithm for solving sets of nonlinear equations.

The schematic of the dual frequency DFB cavity, along with the longitudinal field distribution of the two respective laser wavelengths was calculated by using numerical integration methods explained in detail in [18] and is shown in Fig. 2.

By using numerical integration instead of a Chernoff bound and by reducing the number of codewords to be included in the bound, Divsalar was able to tighten the bound to overcome the cutoff rate limitation.

The models were estimated by means of marginal maximum likelihood estimation using an expectation maximization algorithm and using numerical integration with 15 integration points in Mplus 7.4 (Muthén and Muthén 1998 2012).

Solutions are developed using numerical integration techniques.

We characterized the likelihood surface of each possible resolved tree using numerical integration over branch lengths.

All calculations were performed in Mathematica 8, using numerical integration with 40 recursive bisections when needed.

The area under the SROC curve (AUC) was computed using numerical integration.