ALGEBRAICALLY STABLE TWO-STEP RUNGE-KUTTA METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

We investigate algebraic stability of two-step Runge-Kutta methods [2] for ordinary differential equations using the criterion proposed by Hewitt and Hill [1] for general linear methods. This criterion is based on suitable transformations on the coefficient matrices of the methods under consideration, in such a way that the G-matrix of algebraically stable formulae is the identity matrix. This gives a remarkable improvement, since the determination of the G-matrix is, in general, a nontrivial task. Examples of algebraically stable two-step Runge-Kutta methods possessing the above feature are presented. This work is in collaboration with Zdzislaw Jackiewicz (Arizona State University), Beatrice Paternoster (University of Salerno) and Dajana Conte (University of Salerno). REFERENCES [1] L. L. Hewitt, A. T. Hill. Algebraically stable diagonally implicit general linear methods. Appl. Numer. Math., 60 (6):629–636, 2010. [2] Z. Jackiewicz. General linear methods for ordinary differential equations. John Wiley & Sons, 2009.