On the Removal of Boundary Errors Caused by Runge-Kutta Integration of Nonlinear Partial Differential Equations

It has been previously shown that the temporal integration of hyperbolic partial differential equations 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 p.d.e'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. This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. The second author was supported also by AFOSR 93-0090 ARPA grant N00014-91-J-4016 and NSF grant DMS 9211820