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

Blatov, I.; Strygin, V.

doi:10.1090/S0025-5718-99-01034-0

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
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Math. Comp. 68 (1999), 683-715 Request permission

Abstract:

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

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