On the adaptive computation of integrals of wavelets Original Research Article

The numerical solution of partial differential equations involves the computation of integrals of products of given functions and (derivatives of) trial and test functions. We study this problem using adaptively chosen wavelet bases. Firstly, we reduce this problem to the computation of 1-dimensional integrals and present an algorithm for computing these integrals. Then, we consider appropriate adaptive approximations and study the induced error. Finally, we give numerical results.