A computationally implementable criterion for the solvability of boundary value problems on an infinite domain

摘要

In this note we develop a simple, computationally implementable criterion to determine the solvability of boundary value problems. This criterion for solvability involves converting the boundary value problem to an initial value problem, forming an associated nonlinear boundary constraint, and computing necessary conditions for convergence using a coupled variational initial value problem. Source term and near-field boundary condition effects are explicitly included. The solvability analysis is directly analogous to sampling convergence of a classical shooting method. Analytical and computational examples are provided which give confidence that this methodology is robust and has potentially wide applicability. Extensions to systems of equations are provided and demonstrated for a linear problem.