Sentence examples for solution is singular from inspiring English sources

At the limit where there exists no interval where the solution may be regular, and the solution is singular throughout, we are in the presence of what we call a "fixed" singularity (which again does not hinder integrability).

As expected, the solution is singular near the maximum friction surface.

The solution is singular for all values of, becomes regular between and, and is again singular for.

The exact solution is singular on the origin node and the interfaces Γ are x-axis and y-axis (fixed by the discontinuity of (a x,y))).

For streptomycin no other fundamentally different model could be found that could achieve this (i.e., the solution was singular).

The optimal control solution is usually singular but may be approximated by a bang bang solution.

Second, it is shown that the solution is logarithmically singular at the endpoints.

Another interesting observation is that the error produced by the high order Fourier smoothing method is highly localized near the region where the solution is most singular, while the 2/3 dealiasing method tends to produce oscillations in the entire domain.

The principle of this method is to use the a posteriori error estimate indicator to guide local mesh refinement in computation; in such a way denser meshes are only used where the value of the indicator is larger and the solution is more singular, and consequently the degree of freedoms may be greatly reduced on those only locally refined meshes.

Using Lemma 1.5, we present the existence of at least one positive solution to (1.2) when is singular at and (notice the new Definition 1.1).

The proposed adaptive mesh methods transform a uniform mesh in the logical domain to cluster grid points at the regions of the physical domain where the solution or its derivative is singular or nearly singular.