The properties of a simple fluid, or Ising magnet, confined in an L× ∞ geometry, are studied by means of numerical density-matrix renormalization-group techniques. Whereas the particle-particle potential is short ranged, the wall-particle potential is long ranged decaying as h1/lp for various values of p-integer, where l = 1,2,…,L labels the columns across the strip and h1 is the reduced amplitude of the boundary field. For the shortrange wall-particle potential, according to the Kelvin equation, the bulk coexistence field scales as 1/L for large L; thermodynamics and scaling arguments predict higher-order corrections of the 1/L2 and 1/L5/3 types at partial and complete wetting, respectively. However, at complete wetting for a large range of surface fields and temperatures a correction to scaling of type 1/L4/3 has been found recently. We discuss the influence of long-range wall-fluid potentials on the scaling. Results are obtained for several values of h1 for strips of widths up to L = 690.