Sentence examples for for which an analytic solution is from inspiring English sources

The simplest subclass of viscoelastic fluids is the second grade fluid, for which an analytic solution is possible.

The first test case consists in a two-dimensional fluid compression for which an analytic solution is known.

The method is illustrated with a simple decay model for which an analytic solution is available and subsequently applied to the three mode Kraichnan Orszag problem with favorable results.

The method also works for log-normal data, in which case the SUV values must be log-transformed before simulating thresholds (although for this case an analytic solution is readily available based on the properties of the Gaussian distribution).

An analytic solution is obtained for balloon catheter inflation and deflation, which gives analytically the distribution of curvatures and the maximum strain in the microelectrodes and interconnects.

An analytic solution is also presented which illustrates similarities to other theories.

An analytic solution is obtained for the leading-order evaporation rate.

In a typical computer simulation scenario computers are used to numerically integrate differential equations for which no analytic solution is available.

We tested our scheme through single solitary wave in which the analytic solution is known and extended it to study the interaction of two and three solitary waves and the Maxwellian initial condition where the analytic solutions are unknown during the interaction.

The solver was validated for scalar linear DDEs with one delay and bolus and infusion inputs for which explicit analytic solutions were derived.

However, the same technique can be applied to other nonlinear ordinary differential equations of interest for which their analytic solutions are not available.