This talk focuses on a fundamental problem that arises with high-order time-stepping in initial boundary values problems: a loss of convergence order incurred with multistage Runge-Kutta methods. We will demonstrate the underlying mechanisms that lead to order loss via both examples and numerical analysis, and provide conditions that time-stepping schemes need to satisfy so that order-loss arises or does not arise. We then present a remedy that is based on modifying the boundary conditions. Numerical tests show that this approach recovers full convergence order of the time-stepping schemes. Moreover, the proposed fixes apply to both linear and nonlinear problems.