Numerical Solution of Free Boundary Problems for One-Dimensional Convection-Diffusion Equation

Implicit difference scheme with second order of accuracy both in time and in space is constructed for linear convection - diffusion equation ∂ u/∂ t + c ∂ u/∂ x = μ ∂ ²u/∂ x² . Moving grids are used. Position of a free boundary coincides with a line of grid. Convergence of the difference scheme is examined with the help of analytical solution of a free boundary problem for this equation. It is shown that the algorithm provides second order of accuracy both for solution of the problem and for position of the free boundary.