Search for highly stable two-step Runge–Kutta methods

We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q = p or q = p − 1 . The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.