Sentence examples for made with analytical from inspiring English sources

Comparison is made with analytical results obtained by using the Wiener Hopf technique and the agreement is shown to be excellent.

In order to validate the present spectral approach, comparisons are made with analytical solutions using the Riemann Graves integral operator and with numerical simulations using the finite element approximation.

A comparison of the measurements is made with analytical predictions, which indicates that the experimentally measured deflections agree well with predictions employing both the inscribing and circumscribing yield loci.

For previously published limit cases of the transfer system considered, i.e. for the single transfer of H2S or CO2 accompanied by reversible chemical reaction, a comparison has been made with analytical and approximate solutions of previous authors.

Finally, numerical tests, including migration of radionuclide chains over large distances, are defined and several comparisons are made with analytical and semi-analytical solutions to verify the Monte Carlo method and its related transport code TRACKS on 1D and 3D transport problems.

Comparisons are also made with the analytical equations given in IEC 61508.

Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes.

Advances have been made with the analytical element method (AEM) and discontinuities like impervious barriers, leaky faults and heterogeneities can be incorporated in such models (Strack 1989; Haitjema 1995).

Several examples including the static/dynamic and linear/non-linear heat transfer, the elasticity and the plate bending problems in the polar and cylindrical coordinates are given and comparisons are made with the analytical solutions, such as the Finite Element Method (FEM) and Finite Difference Method (FDM), to demonstrate the degree of accuracy and the convergence of the FBM.

Test solutions were prepared immediately prior to use with culture media from stocks made with CdCl2 (analytical grade, Sigma Chemical, St . Louis MO, USA) dissolved in deionized water.

Due to the lack of analytical solutions for the general cases, the comparison is made with the existing analytical solutions for some special cases.