On best possible order of convergence estimates in the collocation method and galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations

摘要

The collocation method and Galerkin method using parabolic splines are considered. Special adaptive meshes whose number of knots is independetn of the small parameter of the problem are used. Unimprovable estimates in the L_infinity-norm are obtained. For the Galerkin method these estimates are quasioptimal, while for the collocation method they are suboptimal.