Continuation and shooting methods for boundary value problems of Bernstein type

Fixed point continuation methods and shooting methods are combined to produce an effective numerical procedure for solving boundary value problems for nonlinear ordinary differential equations. Typical numerical solution schemes involve an iteration procedure. Continuation methods systematically generate good initial guesses and, when combined with a shooting method and an appropriate update procedure, give systematic means for the numerical solution of nonlinear boundary value problems. This paper concentrates on problems of Bernstein type, which arise naturally in the calculus of variations and in steady-state heat conduction.