Sentence examples for both numerical and approximate from inspiring English sources

In this section we illustrate the general features of the flow using both numerical and approximate analytical solutions.

To understand how the mean escape time, E , varies as a function of model parameters, we consider both numerical and approximate analytic results for comparison.

Figure 5 Comparison of numerical and approximate solutions for fine and coarse grinds.

We describe how numerical and approximate analytical procedures can be developed from the variational principle.

The results of this technique are compared with existing numerical and approximate solutions.

The present method can provide benchmark results for other numerical and approximate methods.

His research has been concentrated on numerical and approximate analytical solution of strongly nonlinear ODEs and PDEs, dynamical systems, and structural deformations.

Numerical and approximate analytical solutions are obtained with two semi-numerical techniques, namely the homotopy perturbation method and the variational iteration method.

Based on the mass and energy conservation equations, numerical and approximate analytical solutions were derived for the air cavern temperature and pressure variations.

It is important to solve this equation for a better understanding of advection and diffusion phenomena in a fractional setting, and for this purpose, numerical and approximate analytical methods are usually required.

Many efforts have been made to develop efficient numerical schemes and approximate methods to deal with the problems of high wavenumbers (i.e., high frequencies) [2 6].