Ten lectures on wavelets
On the wavelet based differentiation matrix
Journal of Scientific Computing
Polynomial splines and wavelets: a signal processing perspective
Wavelets: a tutorial in theory and applications
On the spline-based wavelet differentiation matrix
Applied Numerical Mathematics
The Differentiation Matrix for Daubechies-Based Wavelets on an Interval
SIAM Journal on Scientific Computing
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
SIAM Journal on Numerical Analysis
An adaptive wavelet-vaguelette algorithm for the solution of PDEs
Journal of Computational Physics
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Journal of Computational Physics
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A collection of the Matlab routines that compute the values of the scaling and wavelet functions (&phis;(x) and ψ(x) respectively) and the derivative of an arbitrary function (periodic or non periodic) using wavelet bases is presented. Initially, the case of Daubechies wavelets is taken and the procedure is explained for both collocation and Galerkin approaches. For each case a Matlab routine is provided to compute the differentiation matrix and the derivative of the function f(d) = D(d)f. Moreover, the convergence of the derivative is shown graphically as a function of different parameters (the wavelet genus, D and the scale, J) for two test functions. We then consider the use of spline wavelets.