Exact matching of boundary conditions and incorporation of semiquantitative solution characteristics in initial approximations to boundary value problems

Abstract

Methods are described and illustrated which permit the analyst to construct initial approximations which match virtually any type of boundary condition exactly while also permitting the specification of certain auxiliary constraints such as convexity or the satisfaction of a maximum principle. These methods are based upon transfinite or blending-function interpolation. Such initial approximations are then used to substantially improve the computational efficiency of iterative solution techniques.