Journal of Mathematical Analysis and Applications
(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location . Results of numerical experimentation on viscous flows governed by the Navier-Stokes equations indicate that downstream continuation achieved by applying a second derivative boundary condition at a finite location often provides the least restrictive method of closing the flow .
Original Publication Citation
Cooke, C. H. (1979). Sufficiency of a numerical downstream continuation. Journal of Mathematical Analysis and Applications, 68(2), 599-604. doi:10.1016/0022-247x(79)90140-9
Cooke, Charlie H., "Sufficiency of a Numerical Downstream Continuation" (1979). Mathematics & Statistics Faculty Publications. 118.