On systems of difference equations with wrong boundary conditions

Author:
Stanley Osher

Journal:
Math. Comp. **23** (1969), 567-572

MSC:
Primary 65.67

MathSciNet review:
0247785

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Abstract: Kreiss and Lundquist , 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 and Osher .

**[1]**Heinz-Otto Kreiss and Einar Lundqvist,*On difference approximations with wrong boundary values*, Math. Comp.**22**(1968), 1–12. MR**0228193**, 10.1090/S0025-5718-1968-0228193-X**[2]**Stanley Osher,*Systems of difference equations with general homogeneous boundary conditions*, Trans. Amer. Math. Soc.**137**(1969), 177–201. MR**0237982**, 10.1090/S0002-9947-1969-0237982-4**[3]**Gilbert Strang,*Wiener-Hopf difference equations*, J. Math. Mech.**13**(1964), 85–96. MR**0160335****[4]**Reuben Hersh,*Mixed problems in several variables*, J. Math. Mech.**12**(1963), 317–334. MR**0147790****[5]**Seymour V. Parter,*Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem*, Numer. Math.**4**(1962), 277–292. MR**0148232****[6]**Heinz-Otto Kreiss,*Stability theory for difference approximations of mixed initial boundary value problems. I*, Math. Comp.**22**(1968), 703–714. MR**0241010**, 10.1090/S0025-5718-1968-0241010-7

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0247785-6

Article copyright:
© Copyright 1969
American Mathematical Society