Abstract. An unusual boundary-value problem that arises in a fluidmechanical application is solved to high precision, as a challenge problem in scientific computation. A second-order differential equation must be solved on (0, ∞), subject to boundary conditions that specify only the asymptotic behaviour of the solution at the two ends of the solution domain. In addition, the solution is required to high accuracy to settle a conjecture made by previous authors. The solution is obtained by computing multiple series solutions using Maple. 