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 discr...

There are known methods of approximating the solution of parabolic 2 order systems by solving stochastic differential equations instead. The main idea is based on the fact that a stochastic differential equation defines a diffusion process, generated by an elliptic differential operator on Rd. We propose a difference scheme for the elliptic operator, which possesses the structure of Markov (jum...

A bstract We study the ? -invariant of a Dirac operator on manifold with boundary subject to local conditions help heat kernel methods. In even dimensions, we relate this invariant -invariants operator, while in odd dimension, it is expressed through index operators. stress necessity strong ellipticity condition for applicability our show that Witten-Yonekura are not strongly elliptic, though t...