Many numerical methods used to solve ordinary differential equations or differentialalgebraic equations can be written as general linear methods. The purpose of this thesis is to extend the known convergence results for Runge-Kutta and linear multistep methods to a large class of new promising numerical schemes. In particular, these new results apply to a recently discovered class of multistep Radau type formulas. The excellent stability properties of these methods allow to construct efficient codes for solving a wide spectrum of the above mentioned problems.

The numerical experiments presented at the end of this thesis show that general linear methods can be also of practical use.