Locally one-dimensional difference schemes for the fractional order diffusion equation

Finite-difference schemes for diffusion equation of fractional order with third type boundary conditions in multidimensional domain

“…Taking into consideration the positivity of the expressions in the parentheses (according to Lemma in [5] On the basis of aforementioned Theorem 3 we obtain the estimate for…”

“…In work [4] finitedifference methods of solving boundary value problems for fractional order differential equations were considered. Locally-one-dimensional schemes for fractional order diffusion equations with Dirichlet boundary condition were considered in work [5], locally-one-dimensional schemes for Robin boundary value problem for a fractional order diffusion equation in work [6].…”

Difference schemes for partial differential equations of fractional order

“…In works [26] and [27] there were considered locally-one-dimensional schemes (LOS) for a fractional order diffusion equation in a -dimensional parallelepiped with Dirichlet and Robin conditions, while in [28] the same was made for a fractional heat equation with a concentrated heat capacity. In these works there was proved the convergence of LOS in the uniform metric as 1 2 < 1.…”

Additive difference scheme for two-dimensional fractional in time diffusion equation

“…Contrary to explicit scheme, which is unstable, and implicit scheme [16], which is not numerically efficient, additive scheme is absolutely stable and efficient. Locally onedimensional difference schemes for the fractional order diffusion equation are investigated in [3,9].…”