Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval

Abstract We will describe some results on the numerical solution of differential equations on the interval, in particular with regard to the treatment of boundary conditions. We will concentrate on the elliptic case where we will test some methods specially suited to treat Dirichlet's boundary conditions. Among such methods we will describe a Galerkin method based on the wavelets on the interval of [9] and a wavelet collocation method. For both methods we give some error estimates, along with some numerical results.