High-order finite difference approximations of the solution and the flux to model interface problems in one-dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O ( h 2 ), O ( h 4 ),… accuracy are derived. Numerical integration procedures using Lobatto quadratures for computing three-point schemes of any prescribed order of accuracy are developed. A rigorous rate of convergence analysis is presented. Numerical experiments confirm the theoretical results.