**Convergence
Acceleration of Decomposition by Eigenfunctions of aModel Boundary Value
Problem with a Discontinuous Coefficient**

We consider the convergence acceleration problem of a decomposition by eigenfunctions of a simple model equation with non-smooth coefficient. Two acceleration methods are suggested. The first is analog of well-known acceleration that uses Bernoulli polynomials. The second one is analog of [13]. The comparison of these two methods are given. Numerical results and asymptotic errors of corresponding approximations are presented.