Let us consider non-linear heat conduction equation
, (1)
where
, (2)
with the initial condition ,
and boundary conditions
, (3)
At
. If
, condition (3) is the boundary condition of the second order, but if
, it is the boundary condition of the third order.
Let us introduce analytical grids in space and time:,
,
,
.
Then, define grid functions ,
,
,
,
,
,
,
.