A formulation of asymptotic neutron diffusion theory for numerical calculations is presented which provides in simple ways for physical features not included in the elementary form of the theory. These are: 1) exponential time dependence, which is provided for by a transformation to steady state; 2) effect of surface curvature on the linear extrapolation length, provided for by means of the principal radii of curvature; 3) material discontinuities, provided for by limiting the current at an interface to its free surface value; and 4) prescribed sources and velocity dependence, provided for by a generalization of the number of secondary neutrons per collision. Numerical results are presented showing that the form of time-dependent multigroup neutron diffusion theory thus obtained is more accurate than the ordinary multigroup formulation especially for small or inhomogeneous systems.