A continuing exploration of a decomposed compact method for highly oscillatory wave problems

Jones, Tiffany; Gonzalez, Leonel P.; Guha, Shekhar; Sheng, Qin

doi:10.1016/j.cam.2015.11.044

Cited by 4 publications

(1 citation statement)

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“…Moreover, it can be shown that j 1,1 ≈ 3.8317. Just as before, we discretize the operator A using standard finite differences (see, for example, [20] for more details on doing so for Ω as above). However, in this example we will only consider convergence aspects of the method in the extended variable direction.…”

Section: A Two-dimensional Examplementioning

confidence: 99%

Analysis of an approximation to a fractional extension problem

Padgett

2019

Bit Numer Math

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The purpose of this article is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such approaches in the analysis of time-stepping methods for abstract Cauchy problems, we adopt a similar framework herein. The proposed method differs from many standard techniques, as we approximate the true solution to the abstract problem, rather than solve an associated discrete problem. The numerical method is shown to be consistent, stable, and convergent in an appropriate Banach space. These results are built upon well understood results from semigroup theory. Numerical experiments are provided to demonstrate the theoretical results.

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Section: A Two-dimensional Examplementioning

confidence: 99%