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国际不确定性的量化期刊

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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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ON A POLYNOMIAL CHAOS METHOD FOR DIFFERENTIAL EQUATIONS WITH SINGULAR SOURCES

卷 1, 册 1, 2011, pp. 77-98
DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i1.50
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摘要

Singular source terms in the differential equation represented by the Dirac δ-function play a crucial role in determining the global solution. Due to the singular feature of the δ-function, physical parameters associated with the δ-function are highly sensitive to random and measurement errors, which makes the uncertainty analysis necessary. In this paper we use the generalized polynomial chaos method to derive the general solution of the differential equation under uncertainties associated with the δ-function. For simplicity, we assume the uniform distribution of the random variable and use the Legendre polynomials to expand the solution in the random space. A simple differential equation with the singular source term is considered. The polynomial chaos solution is derived. The Gibbs phenomenon and the convergence of high order moments are discussed. We also consider a direct collocation method which can avoid the Gibbs oscillations on the collocation points and enhance the accuracy accordingly.

对本文的引用
  1. Chakraborty Debananda, Jung Jae-Hun, Efficient determination of the critical parameters and the statistical quantities for Klein–Gordon and sine-Gordon equations with a singular potential using generalized polynomial chaos methods, Journal of Computational Science, 4, 1-2, 2013. Crossref

  2. Chakraborty Debananda, Jung Jae-Hun, Lorin Emmanuel, An efficient determination of critical parameters of nonlinear Schrödinger equation with a point-like potential using generalized polynomial chaos methods, Applied Numerical Mathematics, 72, 2013. Crossref

  3. Yi Lijun, Wang Zhongqing, A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations, Calcolo, 53, 4, 2016. Crossref

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