Sentence examples for average of the solution from inspiring English sources

In the first problem, the QoI is the spatial average of the solution over various regions.

Moreover, the pth moment in time average of the solution to model (8) is discussed in Theorem 4.2.

However, the Riemann solver is only a part of a numerical scheme and non-conservative variables pose extra difficulties for the projection or cell average of the solution.

The m + 1 dispersion coefficients, which define the mth dispersion approximation to the transverse average of the solution of the convective diffusion equation, can be gotten on exacting equality of the first m + 1 moments of the solution and its approximation.

Although it could be set to any reasonable value, including zero, in our case it was set equal to the average of the solutions for the non-ECP classes.

The piecewise linear approximate solution is obtained by approximating the cell average of the analytical solution and the solution slope in every mesh cell.

Basically, we define a constant approximation of the solution gradient in every mesh cell which is expressed by using the cell averages of the solution within the adjacent cells.

Motivated by this work, we introduce overlapping cell averages of the solution at the same discrete time level, and develop a simple alternative technique to control the O(1/Δt) dependence of the dissipation.

The average particle size (Z-average) of the solution was obtained using a Cumulant method.

Estimate statistics: We estimate the expectation of the random solution field with the sample mean (ensemble average) of the approximate solution: E_{M} bigl[U_{mathcal {T}}^{n} bigr]:= frac{1}{M} sum_{k=1}^{M} U_{mathcal {T}}^{k,n}.

The genetic algorithm heuristic was repeated 10 times and the final result is the average of the best solution in each run [49].