Corrected collocation methods for periodic pseudodifferential equations
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We propose an approximation method for periodic pseudodifferential equations, which yields higher convergence rates in Sobolev spaces with negative order than the collocation method. The main idea consists in correcting the usual collocation solution in a certain way by the solution of a small Galerkin system for the same equation. Both trigonometric and spline approximation methods are considered. In most of the cases our convergence result even improves that of the qualocation method.
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