AbstractA fast and accurate method was developed for the integration of large sparse systems of stiff initial value ordinary differential equations. The system is ordered, decoupled and, if necessary, torn into subsystems (also called blocks) which are then solved by orthogonal collocation on finite elements. The size of these elements, or steps, is different for each subsystem and is a function of the stiffness of the set of equations constituting the subsystem. The steps are overlapped for maximum computational efficiency.