  This article extends the theory of dual-consistent summation-by-parts (SBP)
and generalized SBP (GSBP) time-marching methods by showing that they are
implicit Runge-Kutta schemes. Through this connection, the accuracy theory for
the pointwise solution, as well as the solution projected to the end of each
time step, is extended for nonlinear problems. Furthermore, it is shown that
these minimum guaranteed order results can be superseded by leveraging the full
nonlinear order conditions of Runge-Kutta methods. The connection to
Runge-Kutta methods is also exploited to derive conditions under which SBP and
GSBP time-marching methods associated with dense norms are nonlinearly stable.
A few known and novel Runge-Kutta methods with associated GSBP operators are
presented. The novel methods, all of which are L-stable and
algebraically-stable, include a four-stage seventh-order fully-implicit method,
a three-stage third-order diagonally-implicit method, and a fourth-order
four-stage diagonally-implicit method.
