The Lippman-Schwinger equation for the reactance operator is converted into a system of linear equations. By using spline functions the principal-value singularity of the integral kernel can be treated analytically. Throughout this work recurrence relations suitable for automatic computation are derived, relying on the properties of normalized B-splines as given by de Boor. The algorithm developed is recommended for problems with a nonlocal interaction admitting partial wave decomposition. This case occurs, e.g. in the low-energy scattering of two composite nuclei when antisymmetrisation is taken into account. It is shown that addition of a repulsive Coulomb interaction requires no essential modifications of the method. Supplementary applications to bound-state energies and wave functions are given.