Computing connection coefficients of compactly supported wavelets on bounded intervals
Daubechies wavelet basis functions have many properties that make them desirable as a basis for a Galerkin approach to solving PDEs: they are orthogonal, with compact support, and their connection coefficients can be computed. The method developed by Latto et al. to compute connection coefficients does not provide the correct inner product near the endpoints of a bounded interval, making the implementation of boundary conditions problematic. Moreover, the highly oscillatory nature of the wavelet basis functions makes standard numerical quadrature of integrals near the boundary impractical. The authors extend the method of Latto et al. to construct and solve a linear system of equations whose solution provides the exact computation of the integrals at the boundaries. As a consequence, they provide the correct inner product for wavelet basis functions on a bounded interval.
- Research Organization:
- Oak Ridge National Lab., Mathematical Sciences Section, TN (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- AC05-96OR22464
- OSTI ID:
- 661583
- Report Number(s):
- ORNL/TM-13413; ON: DE98007049; TRN: AHC29814%%127
- Resource Relation:
- Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
Similar Records
The use of wavelet transformations in the solution of two-phase flow problems
Wavelet theory for solution of the neutron diffusion equation