False convergence in the nonlinear shooting method

Abstract

We study the concept of false convergence in the nonlinear shooting method for boundary-value problems. We show that false convergence is due to the global error that exists in the Runge-Kutta solution to the associated initial-value problem. We show how the situation can be remedied through the device of global error control in the Runge-Kutta method. We suggest the use of the RKQ algorithm for this purpose.