Exponentially fitted two-step peer methods for oscillatory problems

This paper concerns the construction of a general class of exponentially fitted two-step implicit peer methods for the numerical integration of Ordinary Differential Equations (ODEs) with oscillatory solution. Exponentially fitted methods are able to exploit a-priori known information about the qualitative behaviour of the solution to efficiently furnish an accurate solution. Moreover, peer methods are very suitable for a parallel implementation, which may be necessary in the discretization of Partial Differential Equations (PDEs) when the number of spatial points increases. Examples of methods with 2 and 3 stages are provided. Numerical experiments are carried out in order to confirm theoretical expectations.