Automatic Step Size and Order Controlin Implicit One-Step Extrapolation Methods

摘要

A theory is presented for implicit one-step extrapolation methods for ordinary differentialequations. The computational schemes used in such methods are based on the implicit Runge-Kuttamethods. An efficient implementation of implicit extrapolation is based on the combined step size andorder control. The emphasis is placed on calculating and controlling the global error of the numericalsolution. The aim is to achieve the user-prescribed accuracy in an automatic mode (ignoring round-offerrors). All the theoretical conclusions of this paper are supported by the numerical results obtained fortest problems.