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

It is the purpose of this paper to derive two-step hybrid methods for 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.

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