"On the Order of General Linear Methods"
E. M. Constantinescu
Preprint Version: [pdf]
General linear (GL) methods are numerical algorithms used to solve ODEs . The standard order conditions analysis involves the GL matrix itself and a starting procedure; however, a finishing method (F) is required to extract the actual ODE solution. The standard order analysis and stability are sufficient for the convergence of any GL method. Nonetheless, using a simple GL scheme we show that the order definition may be too restrictive. In this note we explore the order conditions for GL schemes and propose a new definition for characterizing the order of GL methods, which is focused on the final result – the outcome of F – and can provide more effective algebraic order conditions.