Construction of two-step Runge–Kutta methods with large regions of absolute stability

We describe the construction of explicit two-step Runge–Kutta methods of order p and stage order q=p−1 or q=p with large regions of absolute stability. This process is illustrated for the methods of order p=2, and 3 and leads to new methods which are competitive with explicit Runge–Kutta methods of the same order.