Generalized approximations and rapid convergence of solutions of \(m\)-point boundary value problems (Q2372070)

The paper deals with \(m\)-point boundary value problems of second-order on the unit interval. Using the concept of upper and lower solutions of the boundary value problem an existence- and uniqueness result is derived under suitable conditions. Moreover, with an Arzela-Ascoli argument the author shows that there exists a monotone sequence \((w_n)_{n\in\mathbb{N}}\) of solutions of linear problems converging uniformly in the \(C^1\)-norm to the unique solution of the boundary value problem. Under an additional condition locally quadratic convergence takes place.