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
Ia. Blatov et Vv. Strygin, 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, MATH COMPUT, 68(226), 1999, pp. 683-715
The collocation method and Galerkin method using parabolic splines are cons
idered. Special adaptive meshes whose number of knots is independent of the
small parameter of the problem are used. Unimprovable estimates in the L-i
nfinity-norm are obtained. For the Galerkin method these estimates are quas
ioptimal, while for the collocation method they are suboptimal.