Abstract
In this paper we study functionally fitted methods based on explicit two step peer formulas. We show that with $$s$$s stages it is possible to get explicit fitted methods for fitting spaces of high dimension $$2s$$2s, by proving the existence and uniqueness of such formulas. Then, we obtain particular methods with 2 and 3 stages fitted to trigonometric and exponential spaces of dimension 4 and 6 respectively. By means of several numerical examples we show the performance of the obtained methods, comparing them to fitted Adams---Bashforth---Moulton methods with the same order.
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