A fourth order method for y″ = ƒ(x,y, y′)

A fourth order numerical method for solving the general second order differential equation $\text{y″ = ?(x, y, y′)}$ is suggested. This method is self starting, P-stable (when applied to $\text{y″ = ?(x, y)}$), and it involves only two function evaluations per step. Easily calculable and simple truncation error estimates are given, which can be used for automatic error control in computations. The method is illustrated on numerical examples.