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

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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