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 accura cy of the solution because of boundary conditions. A procedure for rem oval of this error in the linear case has been established previously. In this paper we consider hyperbolic PDEs (linear and nonlinear) whos e boundary treatment is accomplished via the simultaneous approximatio n 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-o rder explicit finite-difference scheme.