2019/10/30 by Stanislav Harizanov, Harizanov, Stanislav, Raytcho Lazarov +5
Engineering · Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1910.13865
openalex publication_date 2019/10/30 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this paper we consider one particular mathematical problem of this large\narea of fractional powers of self-adjoined elliptic operators, defined either\nby Dunford-Taylor-like integrals or by the representation through the spectrum\nof the elliptic operator. Due to the mathematical modeling of various non-local\nphenomena using such operators recently a number of numerical methods for\nsolving equations involving operators of fractional order were introduced,\nstudied, and tested. Here we consider the discrete counterpart of such problems\nobtained from finite difference or finite element approximations of the\ncorresponding elliptic problems.\n In this report we provide all necessary information regarding the best\nuniform rational approximation (BURA) rk,\α(t) := Pk(t)/Qk(t) of\nt\α on [\δ, 1] for various \α, \δ, and k. The\nresults are presented in 160 tables containing the coefficients of Pk(t) and\nQk(t), the zeros and the poles of rk,\α(t), the extremal point of\nthe error t^\α - rk,\α(t), the representation of rk,\α(t)\nin terms of partial fractions, etc. Moreover, we provide links to the files\nwith the data that characterize rk,\α(t) which are available with\nenough significant digits so one can use them in his/her own computations.\n