High order discrete method for a class of two-point boundary value problems with periodic boundary conditions
The paper is concerned with second-order ordinary differential equations subject to periodic boundary conditions. A three-point difference scheme is proposed which provides an \(O(h^5)\) local error. In the main part of the article the authors prove that the global error is \(O(h^4)\) (i.e., fourth-order convergence), requiring, in addition, certain bounds for the derivative of the nonlinearity ensuring the stability of the method.
scientific article; zbMATH DE number 774801
scientific article