On systems of difference equations with wrong boundary conditions
HTML articles powered by AMS MathViewer
- by Stanley Osher PDF
- Math. Comp. 23 (1969), 567-572 Request permission
Abstract:
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 $[2]$.References
- Heinz-Otto Kreiss and Einar Lundqvist, On difference approximations with wrong boundary values, Math. Comp. 22 (1968), 1–12. MR 228193, DOI 10.1090/S0025-5718-1968-0228193-X
- Stanley Osher, Systems of difference equations with general homogeneous boundary conditions, Trans. Amer. Math. Soc. 137 (1969), 177–201. MR 237982, DOI 10.1090/S0002-9947-1969-0237982-4
- Gilbert Strang, Wiener-Hopf difference equations, J. Math. Mech. 13 (1964), 85–96. MR 0160335
- Reuben Hersh, Mixed problems in several variables, J. Math. Mech. 12 (1963), 317–334. MR 0147790
- Seymour V. Parter, Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem, Numer. Math. 4 (1962), 277–292. MR 148232, DOI 10.1007/BF01386319
- Heinz-Otto Kreiss, Stability theory for difference approximations of mixed initial boundary value problems. I, Math. Comp. 22 (1968), 703–714. MR 241010, DOI 10.1090/S0025-5718-1968-0241010-7
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 567-572
- MSC: Primary 65.67
- DOI: https://doi.org/10.1090/S0025-5718-1969-0247785-6
- MathSciNet review: 0247785