On the convergence of finite difference methods for a class of two-point boundary value problems with periodic boundary conditions (Q1914653)

For two-point boundary value problems \(y''+ f(x, y)= 0\), \(0\leq x\leq 1\), with periodic boundary conditions the authors present a convergence analysis of an already known three-point two-parameter family of finite difference methods based on one evaluation of \(f\). Under suitable conditions on \(f_y\) and for \(y(x)\), the \(O(h^2)\) convergence is proved.