Tricomi's composition formula and the analysis of multiwavelet approximation methods for boundary integral equations
- Prößdorf, Siegfried
2010 Mathematics Subject Classification
- 41A15 41A17 41A35 41A63 45B05 45E05 45E10 45L10 45M10 47A50 47A75 65N12 65N35 65N38
- 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
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.