Abstract
A shooting method for the numerical solution of a class of nonlinear boundary value problems is analyzed. Dirichlet, Neumann, and Sturm–Liouville boundary conditions are considered, and numerical results are included. The shooting method is well known. What is novel here is the convergence analysis. The usual analyses place stringent hypotheses on the nonlinearity in the differential equation in order to guarantee that all initial value problems for this equation can be solved. Then it is shown that the solution of an appropriate initial value problem also solves the boundary value problem. However, the hypotheses necessarily imposed on the differential equation in this approach are far stronger than those needed to prove an existence and uniqueness theorem for the boundary value problem itself. Our analysis starts with the weaker hypotheses needed to insure existence and uniqueness for the boundary value problem and establishes convergence of the shooting method without additional restrictions.
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