On the spline-based wavelet differentiation matrix
The use of wavelets as a basis set for the numerical solution of partial differential equations is well known. Therefore, the differentiation matrix for a spline-based wavelet basis with periodic and nonperiodic boundary conditions is constructed in this paper. It is shown that a spline-based wavelet basis displays superconvergence when periodic boundary conditions are assumed, but the superconvergence is lost when periodicity is no longer assumed. Furthermore, one can see that spline- based bases generate a class of compact finite difference schemes.
scientific article; zbMATH DE number 758537