Restoring Convergence Order in Explicit Runge-Kutta Integration of Hyperbolic PDE with Time-Dependent Boundary Conditions
This paper proposes a purely spatial remedy for order reduction in explicit Runge-Kutta integration of hyperbolic PDEs with time-dependent boundary conditions by redesigning boundary-adjacent derivative operators to satisfy tableau-dependent algebraic conditions, thereby recovering the nominal convergence order without altering the time integrator.