Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP

2019/10/23 by Petr N. Vabishchevich, Vabishchevich, Petr N.
Computer Science · Mathematics · #35R11 #65D32 #65F60 #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:35R11 #msc:65D32 #msc:65F60

paper · pdf · doi:10.48550/arxiv.1910.11179

13 pages, 2 figures. arXiv admin note: text overlap with arXiv:1905.10838

arxiv created 2019/10/23 · arxiv updated 2019/10/25

Abstract

Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized Gauss-Laguerre formulas are constructed. We examine the effect of key parameters on the accuracy of the approximate solution: the number of nodes of the quadrature and fractional power of the operator. Computational experiments were performed to model two-dimensional problem with a fractional power of an elliptic operator.

Citations

• Approximation of a fractional power of an elliptic operator

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