Central difference schemes and stiff boundary value problems (Q762897)

Under rather restrictive assumptions, the author shows that the solutions to the two-point boundary value problem for a stiff system of ordinary differential equations using centered approximations converge to the solution of the differential equations, provided a certain homogeneous system of differential equations has only the trivial solution. The situation is unclear if these assumptions are not satisfied, one of which is that the original system has no turning points. The analysis concerns methods based on both the trapezoidal rule and implicit Runge-Kutta schemes.