Sentence examples for behaviour of the solution from inspiring English sources

Note that Lemma 1 gives a full description of the limiting behaviour of the solution of unperturbed equation (4).

Due to the corner singularity a singular behaviour of the solution can be expected.

The dependence of the non-linear behaviour of the solution on the wave steepness is discussed.

This case along with all other possible cases of the asymptotic behaviour of the solution (Z(m)) is discussed in Lemma 1, Section 3.

Furthermore, we presented an efficient numerical scheme based on a splitting approach which preserves the qualitative behaviour of the solution of the system.

In the last part, we simulate the stochastic JR-NMM by an efficient numerical scheme based on a splitting approach which preserves the qualitative behaviour of the solution.

The American mathematician Stephen Smale, continuing to develop Poincaré's insights on qualitative properties of differential equations, proved that in some cases the behaviour of the solutions is effectively random.

The actual family of curves (solutions of the differential equation) must have a direction at each point that agrees with that of the line segment of the direction field at that point, so that this method is valuable for gaining some feeling for the behaviour of the solutions in cases in which the equation is difficult to solve or in which the solution is a complicated function.

First, the melt phase behaviour of the solution-blended system was studied by differential scanning calorimetry and transmission electron microscopy.

We illustrate the behaviour of the solutions when increasing the slope μ of the sigmoid.

For results on asymptotic behaviour of the solutions to stochastic difference equations and stabilisation see e.g. [7 11].