Sentence examples for evolution of the solution from inspiring English sources

Then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state.

Moreover, we obtain sharp estimations for the evolution of the solution along the characteristic curves, which enable us to derive the uniform exponential decay of the associated energies.

We describe a fast solver for the inhomogeneous heat equation in free space, following the time evolution of the solution in the Fourier domain.

A dynamical adaption strategy to advance the grid in time and to follow the time evolution of the solution directly exploits the multiresolution representation.

The method is based on a refined analysis on either evolution of the solution u and its gradient ux, that is, Cu±ux or the growth rate of the relative ratio ux/u.

We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level.

In order to see these dynamic properties clearly, we drew the figures for the evolution of the solutions of system (1.2) by using the function dde23 in Matlab; see Figs. 1(a)–1(b).

We notice that the main idea as regards the time-integral nonlocal problems is that only when the time is large, the time-integral term dominates the evolution of the solutions.

In order to see these dynamic properties clearly, we draw the figures for the evolution of the solutions of system (3.5) by using the function ddesd in Matlab; see Figure 1. Figure 1 The phase portrait and time series of system ( 3.5 ).

In Locatelli et al. (2014) [20] a memetic approach, called MDE (Memetic Differential Evolution), for the solution of continuous global optimization problems, has been introduced and proved to be quite efficient in spite of its simplicity.

A two-dimensional model was also developed and validated with the experimental results and two case studies were made at different solution mass flow rates to determine the evolution of the ammonia solution concentration, ammonia absorption rate, bulk solution temperature, gas temperature and solution subcooling throughout the hollow fiber membrane module.