The paper considers the problem of approximation of a function that is a solution of singular perturbation boundary value problem. Such functions have huge boundary layer components, so the applying classical algorithms to them leads to essential errors. We introduce an approach that is a local approximation scheme based on minimal splines on the Shishkin grid, where coefficients of basis functions are calculated as the values of de Boor-Fix type functionals. We also present the results of numerical experiments showing that our approach allows obtaining the approximation of high quality.