On difference approximations with wrong boundary values

Authors:
Heinz-Otto Kreiss and Einar Lundqvist

Journal:
Math. Comp. **22** (1968), 1-12

MSC:
Primary 65.65

DOI:
https://doi.org/10.1090/S0025-5718-1968-0228193-X

MathSciNet review:
0228193

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References | Similar Articles | Additional Information

**[1]**S. V. Parter, "Stabilty, convergence and pseudo-stability of finite-difference equations for an over-determined problem,"*Numer. Math.*, v. 4, 1962, pp. 277-292. MR**26**#5740. MR**0148232 (26:5740)****[2]**P. D. Lax, "On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients,"*Comm. Pure Appl. Math.*, v. 14, 1961, pp. 497-520. MR**26**#3215. MR**0145686 (26:3215)****[3]**W. G. Strang, "Wiener-Hopf difference equations,"*J. Math, and Mech.*, v. 13, 1964, pp. 85-96. MR**28**#3548. MR**0160335 (28:3548)****[4]**H.-O. Kreiss, "Difference approximations for the initial-boundary value problem for hyperbolic differential equations,"*Numerical Solutions of Nonlinear Differential Equations*, Proceedings of a Symposium at the University of Wisconsin (May 1966), edited by Donald Greenspan, Wiley, New York, 1966. MR**0214305 (35:5156)****[5]**M. Y. T. Apelkranz, "On difference schemes for hyperbolic equations with discontinuous initial values." (To appear.)**[6]**H. B. Keller & V. ThomÉE, "Unconditionally stable difference methods for mixed problems for quasi-linear hyperbolic systems in two dimensions,"*Comm. Pure Appl. Math.*, v. 15, 1962, pp. 63-73. MR**28**#1778. MR**0158555 (28:1778)****[7]**P. D. Lax & L. Nirenberg, "On stability for difference schemes; a sharp form of Gårdings inequality,"*Comm. Pure Appl. Math.*, v. 19, 1966, pp. 473-492. MR**0206534 (34:6352)**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0228193-X

Article copyright:
© Copyright 1968
American Mathematical Society