Sentence examples for the present approximation from inspiring English sources

Unlike other harmonic balance methods, all the former global residual errors are introduced in the present approximation to improve the accuracy.

The computational results also reveal that the present approximation can provide accurate estimations for cyclic operations with both short and long cycle periods.

The results of the present approximation were for various reactions compared to the numerical enhancement factors obtained for the model based on the Higbie penetration theory.

To lowest order, agreement is found with Eulerian mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures.

We observe that the present approximation is agreed with numerical solution, and the maximum relative error of present solution is less than −3% in Figure 4.

The present approximation agrees with numerical solution, and the maximum relative error of present solution is less than −3% in Figure 8.

Dotted lines show the present approximations, and solid lines show the results by the FEM. Figure 8 Relative errors of present approximations and the FEM.

The dotted lines show the present approximations, and solid lines show the results by the FEM as time increases.

Dotted lines show the present approximations, and solid lines show the results by the FEM. Figure 4 Relative errors of present solutions and the FEM.

By the comparison of the results obtained using the presented method in Table 2 with the RKM, it is easily found that the present approximations are more efficient.

The results, from the presented approximation, were compared with a more rigorous obtainment method.