A splitting scheme to solve an equation for fractional powers of\n elliptic operators

2015/05/15 by Petr N. Vabishchevich, Vabishchevich, Petr N.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1505.04103

openalex publication_date 2015/05/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

An equation containing a fractional power of an elliptic operator of second\norder is studied for Dirichlet boundary conditions. Finite difference\napproximations in space are employed. The proposed numerical algorithm is based\non solving an auxiliary Cauchy problem for a pseudo-parabolic equation.\nUnconditionally stable vector additive schemes (splitting schemes) are\nconstructed. Numerical results for a model problem in a rectangle calculated\nusing the splitting with respect to spatial variables are presented.\n

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