Sentence examples for by numerical integrations of from inspiring English sources

This distinct behavior of the two types of solutions has been verified by numerical integrations of equation (24).

(68) This condition can be tested only approximately by numerical integrations of equation (66) because the solutions (y(x)) break off oscillating and run away too steeply right before the critical value (2 (2lambda+ 1)) is reached.

For the solutions of the Lane-Emden equations (8) with integer values of (nleq-1), we have verified such a monotonic behavior by numerical integrations of several cases (not shown here).

Flame structures, including formation of species containing two carbon atoms, are measured by gas chromatography of samples withdrawn by fine quartz probes and are calculated by numerical integrations of the conservation equations employing an updated elementary chemical-kinetic data base.

The governing equations are solved analytically and breakthrough curves are determined for the system's parameters by numerical integration of the obtained infinite integral.

Particle ranges may be obtained by (numerical) integration of a suitable stopping-power formula.

Volumes were obtained by numerical integration of the flow signals.

Volume was calculated by numerical integration of V′.

Distance calculated by numerical integration of the speed profile over the duration of the segment.

A fully nonlinear beam-column element estimates element deformations by numerical integration of the section deformations.

The crack growth was simulated by numerical integration of the Paris formula.