On Systems of Difference Equations with Wrong Boundary Conditions

Kreiss and Lundquist $[1]$, have recently obtained certain results about the decay of influence of wrong boundary conditions in overdetermined difference approximations to a hyperbolic partial differential equation. We have extended this result to include systems of hyperbolic partial differential equations in several space variables and their corresponding overdetermined difference approximations. The technique of proof involves examining sections of the resolvent of the difference operator for analyticity within the unit circle as in Kreiss $[6]$ and Osher $[2]$.