Construction of Exponentially Fitted Explicit Peer Methods

It is the purpose of this work to present exponentially fitted explicit two-step peer methods for the numerical integration of ordinary differential equations exhibiting oscillatory solution. We will use a problem oriented approach based on exponential fitting, in order to exploit a-priori known information about the qualitative behavior of the solution. Moreover the constructed methods have inherent method parallelism, therefore they are suitable for the numerical solution of high dimension ordinary differential systems arising for example in the semi-discretization in space of partial differential equations. The construction of methods with 2 and 3 stages is provided. Numerical tests show that the error of EF peer methods is smaller with respect to that of classical peer methods, as the frequency of oscillation increases, thus confirming the effectiveness of this problem-oriented approach