Sentence examples for by the present solution from inspiring English sources

The simulated depth-averaged concentrations in the lower and upper aquifers slightly differ from those predicted by the present solution.

The presented examples for the power law and van Genuchten model demonstrate the accuracy of the present solution by comparing the present results with the results obtained by the FEM.

Numerical procedures have been developed and used to validate the present solution by comparison with available literature results.

The present solution shown by dotted line approximates well with the FEM shown by solid lines in time simulation in Figure 9, and the maximum relative error is −2.0534% in Table 4.

A comprehensive numerical validation was conducted by comparing the present solutions and those developed by Goland and Reissner, Hart-Smith and Oplinger with the results of nonlinear finite element analyses.

The validity of the formulation is confirmed by comparing the present solutions with results available in the literature.

Validity and accuracy of the current method are demonstrated by comparing the present solutions with existing results.

Validity and accuracy of the present formulation are confirmed by comparing the present solutions with the existing results and those obtained from finite element analyses.

The reasonableness of the assumptions of the soil-layer interactions have been verified by comparing the present solutions with two published solutions and a set of well-documented measured pile test data.

The reasonableness of the assumptions of the support plate and soil layer interactions has been verified by comparing the present solutions with dynamic experiments on a full-scale plate in the field.

Performance and accuracy of the present discrete double directors shell model (DDDSM) are confirmed by comparing the present solutions obtained from finite element analyses with the existing results in the literature.