Sentence examples for using the analytic solution from inspiring English sources

This work develops exact finite-difference schemes for the two-dimensional nonlinear coupled viscous Burgers equation using the analytic solution.

The main purpose of this paper is to give an exact finite-difference scheme for the coupled viscous Burgers equations (1) using the analytic solution and give the explicit nonstandard finite-difference schemes on the basis of the exact finite-difference schemes.

Still, the integration time should be adequately long to enable the same-beam method to reduce phase errors and to resolve the ambiguity using the analytic solutions employed in previous work.

The sensitivity matrix (Ai,j) is created using the analytic solutions for photon density in the semi-infinite geometry to obtain the influence of a particular voxel j on every source and detector measurement i: The So is calibration factor while h represents the voxel volume.

Bit population counts are used to fill the contingency table; then we use the analytic solution to Hill's diplotype frequency cubic equation [ 24, 25 ] and only compute and compare log likelihoods in this step when multiple solutions to the equation are in the valid range.

"It removes the barrier to using the analytics solutions they should be using, but aren't, because it's a pain to set up," he says.

Using the analytic form of the solution, it is shown that the observed discrepancy is related to interaction between the damped hydrodynamic mode and a downstream propagating higher order acoustic mode.

A semi-analytic method for matching the boundary conditions is proposed by using the analytic form of the extremal solutions and a closed form solution for the exponential map.

We develop an explicit closed-form solution to the boundary-value problem using the analytic element method.

Hussnain et al. [22] in 2012 used HAM for the analytic solution of second grade fluid in the rotating system between two horizontal plates in the presence of a transverse magnetic field.

We compare our numerical solution to the analytic solution using the error defined by (18).