Implicit–explicit two–step peer methods with RK stability for implicit part

We develop a new family of implicit–explicit (IMEX) schemes appropriate for dealing with the systems of differential equations including two non–stiff and stiff parts on the right–hand side. The proposed IMEX schemes are a combination of \(\varvec{s}\) $\mathit{s}$ -stage explicit and implicit diagonally implicit two–step peer methods, in which the implicit part of the methods is \(\varvec{A}\) $\mathit{A}$ – or \(\varvec{L}\) $\mathit{L}$ –stable and also equipped with Runge–Kutta stability property. The order conditions of this class of IMEX schemes are derived for the methods of orer \(\varvec{p}=\varvec{s}\) $\mathit{p}=\mathit{s}$ and their stability behavior is analyzed. Some examples of the methods with \(\varvec{p}=\varvec{s}\) $\mathit{p}=\mathit{s}$ up to order five are constructed and the performance of the proposed methods is investigated by giving the results of some numerical experiments.