S-Stability properties for generalized Runge-Kutta methods

Summary A class of generalized Runge-Kutta methods is considered for the numerical integration of stiff systems of ordinary differential equations. These methods are characterized by the fact that the coefficients of the integration formulas are matrices depending on the Jacobian, or on an approximation to the Jacobian. Special attention is paid to stability aspects. In particular, theS-stability properties of the method are investigated. The concept of internal stability is discussed. Internal stability imposes conditions on intermediate results in the Runge-Kutta scheme. Some numerical examples are discussed.