Resumen de Extending convergence results of Runge–Kutta methods for stiff semi linear initial value problems

Manuel Calvo Pinilla, Severiano González Pinto, Juan Ignacio Montijano Torcal

• In this paper some convergence results for Runge–Kutta methods applied to semi–linear variable coefficients differential systems with the stiffness contained in the linear part and under some assumptions on the relative variation of the jacobian matrix are derived. Previous results on this subject given by the authors in BIT 40, 4 (2000), pp. 611–634, are generalised. In particular, it is shown that some non B–stable methods such as those of the Lobatto IIIA family and some DIRK methods that have been used in practical problems are convergent of order greater or equal than the stage order for this kind of problems. Some numerical examples are presented to illustrate the theory.