Boundary-value problems for the heat conduction equation with a fractional derivative in the boundary conditions. Difference methods for numerical realization of these problems

Problems with free boundaries and nonlocal problems for nonlinear parabolic equations

“…In [17], the well-posedness of the statements of similar nonlinear initial boundary-value problems was proved, one-parameter families of difference schemes were constructed, and it was shown that these schemes are stable and converge in the uniform metric.…”

“…The realization of these conditions leads to the ordered stratification of the domain f2(t) by the level surfaces u (x, t)= const. We represent such level surfaces in the form [I2, t5] z = z(x,y,u,t), (17) where x, y, and z are the Cartesian coordinates.…”

“…problem ( Constructive methods for the solution of the above-mentioned one-dimensional problems connected with the Rothe methods, the method of integral equations, and some special approximations were considered in [2,8,9,15,[17][18][19][20][21][22].…”

Untitled

“…Equations with fractional derivatives appear in studying processes of filtering of liquids or gases in porous media and transport of salts and water in soil [1], in modeling physical phenomena such as diffusion in fractal media [6], and in estimating heat processes on the basis of a thermophysical one-dimensional model of a two-layer cover-base system, with the help of a nonstationary heat flow [5].…”