Local error estimation for singly-implicit formulas by two-step Runge-Kutta methods

In this paper it is shown that the local discretization error of s-stage singly-implicit methods of order p can be estimated by embedding these methods into s-stage two-step Runge-Kutta methods of order p+1, where p=s or p=s+1. These error estimates do not require any extra evaluations of the right hand side of the differential equations. This is in contrast with the error estimation schemes based on embedded pairs of two singly-implicit methods proposed by Burrage.