Implicit Runge-Kutta processes

If the function f(y) satisfies a Lipschitz condition and h is sufficiently small, then the equations defining g(1>, g(2), • • • , gw have a unique solution which may be found by iteration (see Appendix).t It will be assumed throughout that f (y) and all its derivatives exist and are continuous so that the Taylor expansions for y and y may be terminated at any term with an error of the same order as the first term omitted.