A NUMERICAL STUDY OF THE HOMOGENEOUS ELLIPTIC EQUATION WITH FRACTIONAL BOUNDARY CONDITIONS Academic Article

abstract

• 2017 Diogenes Co., Sofia. We consider the homogeneous equation Au = 0, where A is a symmetric and coercive elliptic operator in H 1 () with bounded domain in d . The boundary conditions involve fractional power , 0 < < 1, of the Steklov spectral operator arising in Dirichlet to Neumann map. For such problems we discuss two different numerical methods: (1) a computational algorithm based on an approximation of the integral representation of the fractional power of the operator and (2) numerical technique involving an auxiliary Cauchy problem for an ultra-parabolic equation and its subsequent approximation by a time stepping technique. For both methods we present numerical experiment for a model two-dimensional problem that demonstrate the accuracy, efficiency, and stability of the algorithms.

authors

• Lazarov, Raytcho

published proceedings

• FRACTIONAL CALCULUS AND APPLIED ANALYSIS

author list (cited authors)

• Lazarov, R., & Vabishchevich, P.

citation count

• 10

complete list of authors

• Lazarov, Raytcho||Vabishchevich, Petr

publication date

• January 2017

publisher

• Springer Nature  Publisher

published in

• Journal of Fractional Calculus and Applied Analysis  Journal

keywords

• Fractional Boundary Conditions
• Fractional Partial Differential Equations
• Numerical Methods For Fractional Powers Of Elliptic Operators
• Ultra-parabolic Equations

Digital Object Identifier (DOI)

• 10.1515/fca-2017-0018

start page

• 337

end page

• 351

volume

• 20

issue

• 2

URL

• http://dx.doi.org/10.1515/fca-2017-0018