APPLYING OPTIMAL DIFFERENCE GRIDS TO PROBLEMS WITH SINGULAR PERTURBATIONS

On the basis of an algorithm which calculates optimal grids with two free parameters, the boundary intervals, a composite non-uniform grid is constructed for a problem with a singular perturbation. The grid is adapted to the problem by suitable choice of the free parameters. It is proved that the solutions of the classical difference scheme at the grid points converge uniformly to the solution of the initial singularly perturbed problem relative to the perturbation parameter epsilon.