Spline-wavelet solution of singularly perturbed boundary problem

Abstract

Boundary or interior layers typically appear in singularlyperturbed boundary problems. Solution gradients are very sharp inthese regions, and it seems natural to use wavelets to obtainnumerical solution. As layers are usually positioned onboundaries, wavelets have to be modified appropriately. In thispaper the collocation method based on spline-wavelets is derivedand tested on simple linear one-dimensional singularly perturbedboundary problem.