Numerical solution of the heat equation in unbounded domains using quasi-uniform grids

Numerical solutions of the heat equation on the semi-infinite interval in one dimension and on a strip in two dimensions with nonlinear boundary conditions are investigated. At the space discretization with respect to the variable on the semi-infinite interval, we use quasi-uniform mesh with finite number of intervals. Convergence results are formulated. Numerical experiments demonstrate the efficiency of the approximations. The results are compared with those, obtained by the well known method of artificial boundary conditions.