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The latter movements matched the analytical predictions of soil displacements caused by the groundwater oscillations.
It was observed that the results of the numerical analysis matched the analytical results obtained by Spangler's equation for wider trench configuration.
The method was numerically validated and matched the analytical function describing the pressure amplitude along the axis of a cylindrical transducer with a root-mean-square error of less than 2%.
The standard deviation matched the analytical solution to the chemical master equation closely, and the mean behavior also behaved as expected (20 of 20 points fell in the 95% CI).
It can be seen that TIM-OS correctly simulated the focusing effect of the spherical lens and the wave front of the light pulse on the "Z" axis matched the analytical expected frontier well, which can be computed by the light speed in glass, air, and tissue.
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Numerical simulations match the analytical results well.
Moreover, numerical simulations match the analytical results well.
The simulation results match the analytical results very well.
Simulation results are found to closely match the analytical results.
A simulation using a numerical Euler integration technique will be used to match the analytical model.
Numerical examples are given to verify the performance of these proposed methods, and the results match the analytical values well.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com