Explicit Runge-Kutta formulas with increased stability boundaries

A survey of the main results is given of our work of the last years on explicit Runge-Kutta methods for the integration of ordinary or partial differential equations. Three classes of integration formulas are presented which have second, third and fourth order accuracy, respectively. These methods are characterized by their limited storage requirements and by the possibility to adapt the characteristic root of the method to the problem under consideration. They may be used for the integration of parabolic, of hyperbolic and of stiff differential equations.