1. The integration of an analytical expression or of discrete or continuous data by approximate numerical methods. These methods usually involve fitting sample curves to successive groupings or sets of the data and performing the integration step-wise. 2. A solution of the governing equations of hydrodynamics by numerical methods. The numerical solutions are carried out with the aid of computers ranging from desktop workstations to the most powerful computers available. The latter are required, in particular, for the timely production of operational global weather forecasts. See finite differencing, finite-element model, spectral model.