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The first is that this method changes the computational grid in order to maintain a uniform approximation.
Under these conditions a uniform approximation of order (O(h^{4})) (h is the grid size) is obtained for the solution of the Dirichlet problem on a square grid, its first and pure second derivatives, by a simple difference scheme.
As we have already mentioned, the solution technique utilizing a uniform approximation of the wave equation, what we discussed above can also be used to treat the X mode.
The variation of each component of the electric field and the total electric field intensity of the standing wave pattern under a specific density profile are calculated by means of a uniform approximation, which is applied throughout the region near the reflection point.
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Garzón et al. [9] proved a strong uniform approximation with a rate of convergence for subfractional Brownian motion by means of transport processes.
Moreover, the model in [32] is a locally uniform approximation of the camera shake blurring model, while GAC can be strictly equivalent with the geometric model in [30].
By incorporating the fundamentals of Floquet theory, an almost uniform approximation to the entire spectrum of the maximal extension is obtained, as opposed to an approximation of a few selected elements.
In other words, we have chosen a C 2 uniform approximation of the truncation ( v − V R ) + / ( V F − V R ) with x + = max ( x, 0 ) obtained by integrating twice a smooth suitable approximation of the δ ( V − V R ) / ( V F − V R ).
Finally, the fourth one consists of solution of a fourth-order system of a supplementary problem to obtain a more or less uniform approximation of thickness-wise distributions of deformations in the plate.
Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011).
A significant implication of this observation is that solution of the present auxiliary problem is necessary so as to obtain a more or less uniform approximation to thickness-wise distributions of deformations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com