Step 5: Verify and test the solution

To conclude the analysis, the solutions found in Steps 3 and 4 will be compared. Using the same set of parameters as in Step 3, the sag time is found to be:

> subs( DOvals, tcrit );

> sag_time := evalf( %, 3 );

This is almost 0.01 days (about 15 minutes) later, and 0.2 km further downstream, than was predicted from the graphical solution. This discrepancy between the floating-point and graphical results can be reduced, as mentioned in Step 4, by zooming in on the region around the sag time. However, an accurate approximation is difficult to obtain because the curve is essentially horizontal for a relatively long period of time in the neighborhood of the sag time. The result obtained analytically in Step 4 ( = 0.585 days ) does not suffer from this difficulty; it gives the true sag time, within the accuracy of the model (and parameter values).

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Comparison of floating-point evaluation with subs and eval