The Order of Convergence of General Linear Methods for Ordinary Differential Equations
Gregory S. Cooper · SIAM Journal on Numerical Analysis · 1978
General linear methods, used for the numerical solution of ordinary differential equations, may be characterized by a pair of matrices $(A,B)$. In this article, the order of convergence of such methods is obtained by defining a sequence of norms associated with an order vector. The order of consistency is defined in terms of these norms and it is shown that this definition is sufficient to establish the order of convergence of conventional stable methods. The general case requires additional properties which are also defined in terms of the norms. Some examples of unconventional methods are given.