Numerical solution of time-dependent problems with fractional power elliptic operator
arXiv:1704.03851 · doi:10.1134/S0965542518030120
Abstract
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, standard two-level schemes are used. The approximate solution at a new time-level is obtained as a solution of a discrete problem with the fractional power of the elliptic operator. A Pade-type approximation is constructed on the basis of special quadrature formulas for an integral representation of the fractional power elliptic operator using explicit schemes. A similar approach is applied in the numerical implementation of implicit schemes. The results of numerical experiments are presented for a test two-dimensional problem.
25 pages, 13 figures, 6 tables. arXiv admin note: text overlap with arXiv:1510.08297, arXiv:1412.5706