S. Abarbanel et al., ON THE REMOVAL OF BOUNDARY ERRORS CAUSED BY RUNGE-KUTTA INTEGRATION OF NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS, SIAM journal on scientific computing, 17(3), 1996, pp. 777-782
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.