Expansion of Step-Transition Operator of Multi-Step Method and Its Applications (I) (Journal of Computational Mathematics, 2002)
We expand the step-transition operator of any linear multi-step method with order $s \ge 2 \ {\rm up} \ {\rm to} \ O({τ^{s+5}})$. And through examples we show how much the perturbation of the step-transition operator caused by the error of initial value is.
Keywords: Multi-step method; Step-transition operator; Expansion.