  We apply Runge-Kutta methods to linear partial differential-algebraic
equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$,
where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under
certain conditions the temporal convergence order of the fully discrete scheme
depends on the time index of the partial differential-algebraic equation. In
particular, fractional orders of convergence in time are encountered.
Furthermore we show that the fully discrete scheme suffers an order reduction
caused by the boundary conditions. Numerical examples confirm the theoretical
results.
