Comparing Shannon to autocorrelation-based wavelets for solving singularly perturbed elliptic BV problems

A Shannon wavelet algorithm (essentially F. Stenger's sinc-Galerkin collocation method) is proposed to solve typically singularly perturbed ordinary and elliptic boundary-value problems. The method is shown to be effective and competitive with respect to the autocorrelation-based method in a number of examples, in one and two dimensions, when the smallness parameter becomes smaller and smaller. Advantages can be expected to be even more pronounced when the ''fast sinc transform'' is used.