A transformation relating explicit and diagonally-implicit general linear methods Original Research Article

Using the “inherent Runge–Kutta stability” property, it is possible to construct diagonally-implicit general linear methods with stability regions exactly the same as for Runge–Kutta methods. In addition to A-stable methods found in this way, it is also possible to construct explicit methods with stability regions identical to those of explicit Runge–Kutta methods. A transformation is introduced that links these two types of methods but with a modified form of the order conditions. This makes it possible to greatly widen the family of both explicit and diagonally-implicit methods possessing Runge–Kutta stability.