Exponentially fitted two-step hybrid methods for y″=f(x,y)y″=f(x,y)

It is the purpose of this paper to derive two-step hybrid methods for y″=f(x,y)y″=f(x,y), with oscillatory or periodic solutions, specially tuned to the behaviour of the solution, through the usage of the exponential fitting technique. The construction of two-step exponentially fitted hybrid methods is shown and their properties are discussed. Some numerical experiments confirming the theoretical expectations are provided.