Spline-wavelet solution of singularly perturbed boundary problem

Desanka RadunoviŠ

Boundary or interior layers typically appear in singularly perturbed boundary problems. Solution gradients are very sharp in these regions, and it seems natural to use wavelets to obtain numerical solution. As layers are usually positioned on boundaries, wavelets have to be modified appropriately. In this paper the collocation method based on spline-wavelets is derived and tested on simple linear one-dimensional singularly perturbed boundary problem.