Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction-Diffusion Equation with Boundary Layers
A two-grid method for the elliptic equation with a small parameter ε multiplying the highest derivative is investigated. The ε-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with ε-uniform interpolation formula is used. To increase the accuracy of the scheme, the Richardson extrapolation in the two-grid method is applied. The results of numerical experiments are discussed. Various iterative methods for implementation of the two-grid algorithm are suggested.