A Note on Preconditioning for Singularly Perturbed Problems Discretized by Wavelets

摘要

In the modeling of boundary value problems for singularly perturbed differential equations, one can observe boundary and interior layers whose width can be arbitrary small. To solve such types of problems a lot of methods were proposed. In this contribution, we focus on methods based on wavelets. Using wavelet discretization of singularly perturbed two-point boundary value problems, one can observe that the condition numbers of the arising stiffness matrices are growing with decreasing parameter ε. We show here that a matrix splitting can stabilize the condition numbers of the stiffness matrices for small values of parameter ε. Numerical examples are given.