On the construction of diagonally implicit two–step peer methods with RK stability

Abstract

In this paper, diagonally implicit two–step peer methods for the numerical solution of initial value problems of order ordinary differential are divided into four types including the combination of explicit and implicit methods in a sequential or parallel environments. In this class of the methods, construction of implicit methods equipped with Runge–Kutta stability property together with A– or L–stability are investigated and examples of such methods are given up to order five. Finally, the efficiency and accuracy of the proposed methods are verified by applying them on some well–known stiff problems.