spa Gonzalez-Pinto, S. Pérez-Rodríguez, S. Montijano, Juan I. Implementation of high-order implicit Runge-Kutta methods high-order implicit runge-kutta methods In this paper, we develop single-Newton iterative schemes for the solution of the stage equations of some implicit Runge-Kutta methods such as the four-stage Gauss and Radau IIA methods and the five-stage Lobatto IIIA formula. We also compare the implementation cost of these schemes with the simplified-Newton iteration and we present some numerical experiments on some well-known stiff test problems to show that the proposed iterations are reliable and efficient. 2009-05-07T11:31:12Z http://zaguan.unizar.es/record/3270 info:eu-repo/semantics/publishedVersion Zaragoza Researchers Students Librarians