Removal of Boundary Errors Caused by Runge-Kutta Integration of Non-LinearPartial Differential Equations

摘要

It has been previously shown that the temporal integration of hyperbolic partialdifferential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.