Sentence examples for singularity of the solution from inspiring English sources

A singularity of the solution at the initial point in time is discussed.

(ii) In order to eliminate the singularity of the solution for the case of large injection, the analytical solution is constructed by the Lighthill method.

In order to eliminate the singularity of the solution for the case of large injection, the analytical solution is constructed by the Lighthill method.

Singularity or near singularity of the solution equation set provides specific information about the node motion which can be used to improve the solution.

Starting from the shock front the numerical integration is carried out until the singularity of the solution ρ ′ ( 1 - β ) + M A - 2 2 1 - 1 β 2 + M A - 2 h ′ β - ρ ′ ( 1 - u ′ ) 2 = 0 (4.1)is reached.

Starting from the shock front, the numerical integration is carried out until the singularity of the solution βγ p ′ 1 − β + M A − 2 1 − 1 β 2 − M A − 2 h ′ β − ρ ( 1 − u ′ ) 2 = 0, Open image in new window (4.1). is reached.

One of the keys to make AFEM work is that the value of the error estimate indicator has to be highly positively correlated to the singularity of the solutions to be approximated.

We compute the singularities of the solution of the Birkhoff Rott equation that governs the evolution of a planar periodic vortex sheet.

Such asymptotic results in singularities of the solution to the first and the second Cauchy problems at the point of application of the delta pulse, whereas the solution to the source problem does not have singularity.

Finally, the authors in [6, 7, 10, 11, 22] use the Tikhonov regularization to identify the implied volatility, while it may over-smooth the exact solution and may not preserve the singularities of the solution well when the exact solution has some singularities.

Furthermore, the asymptotic solutions are constructed by the Lighthill method, which eliminates the singularity of the similarity solution, for large injection and by the matching theorem for the suction Reynolds number, respectively.