Přehled o publikaci

Many problems in science and technology can be modeled by boundary value problems for singularly perturbed differential equations. In the modeling of these processes, 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 condition numbers of arising stiffness matrices are growing with decreasing parameter epsilon when an unsymmetric part starts to dominate. We propose here a new simple diagonal preconditioning which significantly improves condition numbers of stiffness matrices for small value of parameter epsilon. Numerical examples are given.