English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we consider one particular mathematical problem of this largearea of fractional powers of self-adjoined elliptic operators, defined eitherby Dunford-Taylor-like integrals or by the representation through the spectrumof the elliptic operator. Due to the mathematical modeling of various non-localphenomena using such operators recently a number of numerical methods forsolving equations involving operators of fractional order were introduced,studied, and tested. Here we consider the discrete counterpart of such problemsobtained from finite difference or finite element approximations of thecorresponding elliptic problems.  In this report we provide all necessary information regarding the bestuniform rational approximation (BURA) $r_{k,\alpha}(t) := P_k(t)/Q_k(t)$ of$t^{\alpha}$ on $[\delta, 1]$ for various $\alpha$, $\delta$, and $k$. Theresults are presented in 160 tables containing the coefficients of $P_k(t)$ and$Q_k(t)$, the zeros and the poles of $r_{k,\alpha}(t)$, the extremal point ofthe error $t^\alpha - r_{k,\alpha}(t)$, the representation of $r_{k,\alpha}(t)$in terms of partial fractions, etc. Moreover, we provide links to the fileswith the data that characterize $r_{k,\alpha}(t)$ which are available withenough significant digits so one can use them in his/her own computations.

The Best Uniform Rational Approximation: Applications to Solving Equations Involving Fractional powers of Elliptic Operators