Sentence examples for by presenting some numerical from inspiring English sources

We show the effectiveness of the measures by presenting some numerical examples.

We end this paper by presenting some numerical simulations for the population density model that we introduced, which are compared to direct Monte Carlo simulations.

Finally, the efficiency, applicability, and high accuracy of the suggested algorithms are demonstrated by presenting some numerical examples accompanied with comparisons with some other existing techniques discussed in the literature.

This section is devoted to presenting some numerical results obtained by the application of the two proposed numerical methods.

In Section 3, we present some numerical results by using the test problems in [17].

In this section, we present some numerical examples by using Maple 11.

In this section, we present some numerical results by implementing our proposed algorithm in a game and a traffic problem, which demonstrate the application and performance of our proposed algorithm.

In this section, we present some numerical solutions by using Matlab 7.0 to verify the analytical predictions obtained in the previous section, using the hybrid control strategy to gain control of the Hopf bifurcation of a delayed Lotka-Volterra predator-prey system (1.2).

We validate the approach by presenting various numerical tests.

Then, we construct a numerical scheme for this model and validate the approach by presenting various numerical tests.

The effectiveness of the method is demonstrated by presenting a numerical example of a non-linear system subject to stochastic ground acceleration.