Finite-difference approximation of the boundary conditions of the second and third order for the nonlinear heat conduction equation

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 , , , , , , , .

Continue reading