THE SPLINE-GALERKIN METHOD FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS ON PIECEWISE UNIFORM GRID

The authors consider the spline-Galerkin method on systems of singularly perturbed equations of the first order. The results obtained earlier by one of the authors for adaptive grids N. S. Bahvalova are applied for traditional in the last decade grid by G. I. Shishkin. Error estimates of approximate solutions of third order of accuracy that are conditionally uniform and asymptotically sharp in contrast to similar estimates of the error in the method of spline collocation.