The eigenvalue problem (1) is considered and for any eigenvalue $\lambda_{k}$ an increasing sequence $\lambda_{h}^{(n)}$ converging to $\lambda_{k}$ is constructed. The approximation error $\lambda_{h}-\lambda_{h}^{(n)}$is estimated. The $\lambda_{h}^{(n)}$ are obtained as eigenvalues of a differential equation with piecewise constant coefficients.