Solution of the Dirichlet problem for a singularly perturbed reaction-diffusion equation in a square on a Bakhvalov grid

The Dirichlet problem for a singularly perturbed reaction-diffusion equation in a square is solved with the help of the classic five-point difference scheme and a grid that is the tensor product of 1D Bakhvalov grids. Without imposing additional matching conditions in the corners of the domain, it is shown that the grid solution to the problem has the accuracy O(N -2) in the norm L ∞ h, where N is the number of grid nodes along each direction. The accuracy is uniform with respect to a small parameter. A simulation confirms the theoretical prediction. © 2009 Allerton Press, Inc.