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Using the refinement equation for evaluating integrals of wavelets. (English) Zbl 0773.65006

Using stationary subdivision schemes the wavelet Galerkin method for partial differential equations is studied. One of the main results is to identify the integrals of the Galerkin method as components of the unique solution of a certain eigenvector-moment problem associated with the coefficients of the refinement equation. Asymptotic expansions for the corresponding subdivision schemes are also given. Numerical results are not presented.

MSC:

65D20 Computation of special functions and constants, construction of tables
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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