On the stability of a classical second order method for solving a class of two-point boundary value problems

摘要

We consider the stability of a classical second order method for the class of two-point boundary value problems: y(4) + f(x, y) = 0, y(0) = A1, y(1) = B1, y″(0) = A2, y″(1) = B2, A1, A2, B1 and B2 being constants. It is shown that, for sufficiently small h, this well-known method is stable for all ∂f/∂y satisfying −π4 < ∂f/∂y < 4K4, where K is the smallest positive root of tan K = tanh K, K = 3.9266.