On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations

The temporal integration of hyperbolic partial differential equations (PDEs) has been shown to lead sometimes to the deterioration of accuracy of the solution because of boundary conditions. A procedure for removal of this error in the linear case has been established previously. In this paper we consider hyperbolic PDEs (linear and nonlinear) whose boundary treatment is accomplished via the simultaneous approximation term (SAT) procedure. A methodology is presented for recovery of the full order of accuracy and has been applied to the case of a fourth-order explicit finite-difference scheme.