On a Method of Solving Sensitive Boundary Value Problems

Nonlinear two-point boundary value problems have always been difficult to solve. The difficulty is compounded if the problem tends to be inherently unstable. This paper describes an algorithm for solving such sensitive boundary value problems. The procedure is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele. The method is demonstrated by solving Troesch's problem and a singular perturbation problem.