A splitting scheme to solve an equation for fractional powers of elliptic operators
Provides a novel numerical method for efficiently solving fractional elliptic equations, relevant to computational mathematics and physics.
The paper develops unconditionally stable splitting schemes for solving equations with fractional powers of elliptic operators, demonstrating effectiveness on a model problem in a rectangle.
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.