Abstract
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an auxiliary Cauchy problem for a pseudo-parabolic equation. Unconditionally stable vector-additive schemes (splitting schemes) are constructed. Numerical results for a model problem in a rectangle calculated using the splitting with respect to spatial variables are presented.
Keywords: Elliptic Operator Equation; Fractional Power of an Operator; Two-Level Schemes; Splitting Schemes; Stability of Difference Schemes
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 14-01-00785, 15-01-00026
Received: 2015-08-08
Revised: 2015-10-30
Accepted: 2015-11-03
Published Online: 2015-11-11
Published in Print: 2016-01-01
© 2016 by De Gruyter
