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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 e. We show here that a matrix splitting can stabilize the condition numbers of the stiffness matrices for small values of parameter e. Numerical examples are given