Initial value problems: numerical methods and mathematics

AbstractA number of questions and results concerning Runge-Kutta and general linear methods are surveyed. These include order conditions and order bounds for Runge-Kutta methods, the A-stability of implicit Runge-Kutta methods based on Gaussian quadrature and transformation methods of implementation which lead to singly-implicit methods. The sections dealing with general linear methods include a discussion of the order conditions and an algebraic structure for carrying out order analyses as well as an introduction to a special function associated with parallel methods for stiff problems