This research activity is a one week workshop on 'Asymptotic Analysis and Numerical Solution of Nonlinear Differential Equations' to be held at Argonne National Laboratory in March of 1990. The workshop will be devoted primarily to nonlinear partial differential equations that, because of the occurrence of a large or small parameter or critical parameter values, are amenable to asymptotic analysis. Emphasis will be placed on equations that arise in the context of nonlinear transport and diffusion phenomena. This research workshop will focus on certain problems in applied analysis. The problems typically arise in the modeling of physical phenomena. Examples are the modeling of fluid flow with critical Reynolds number, flow through porous media, and combustion phenomena. The goal of the workshop is to advance recent progress in the synthesis of asymptotic analysis and the numerical solution of singular perturbation problems.