WIAS Preprint No. 395, (1998)

Tricomi's composition formula and the analysis of multiwavelet approximation methods for boundary integral equations



Authors

  • Prößdorf, Siegfried

2010 Mathematics Subject Classification

  • 41A15 41A17 41A35 41A63 45B05 45E05 45E10 45L10 45M10 47A50 47A75 65N12 65N35 65N38

Keywords

  • Tricomi's composition formula, collocation methods, defected splines, Galerkin-Petrov methods, multidimensional singular integral operators, multiscaling functions, multiwavelets, numerical symbol, pseudodifferential operators, stability conditions, superapproximation, symbol calculus

DOI

10.20347/WIAS.PREPRINT.395

Abstract

The present paper is mainly concerned with the convergence analysis of Galerkin-Petrov methods for the numerical solution of periodic pseudodifferential equations using wavelets and multiwavelets as trial functions and test functionals. Section 2 gives an overview on the symbol calculus of multidimensional singular integrals using Tricomi's composition formula. In Section 3 we formulate necessary and sufficient stability conditions in terms of the so-called numerical symbols and demonstrate applications to the Dirchlet problem for the Laplace equation.

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