Stability theory of difference approximations for mixed initial boundary value problems. II

Authors:
Bertil Gustafsson, Heinz-Otto Kreiss and Arne SundstrÃ¶m

Journal:
Math. Comp. **26** (1972), 649-686

MSC:
Primary 65M10

MathSciNet review:
0341888

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Abstract: A stability theory is developed for general difference approximations to mixed initial boundary value problems.

The results are applied to certain commonly used difference approximations which are stable for the Cauchy problem, and different ways of defining boundary conditions are analyzed.

**[1]**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**[2]**H.-O. Kreiss,*Difference approximations for initial boundary-value problems*, Proc. Roy. Soc. London Ser. A**323**(1971), 255–261. A discussion on numerical analysis of partial differential equations (1970). MR**0501979****[3]**Heinz-Otto Kreiss,*Difference approximations for the initial-boundary value problem for hyperbolic differential equations*, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966) John Wiley & Sons, Inc., New York, 1966, pp. 141–166. MR**0214305****[4]**Heinz-Otto Kreiss,*Initial boundary value problems for hyperbolic systems*, Comm. Pure Appl. Math.**23**(1970), 277–298. MR**0437941****[5]**Stanley Osher,*Stability of parabolic difference approximations to certain mixed initial boundary value problems*, Math. Comp.**26**(1972), 13–39. MR**0298990**, 10.1090/S0025-5718-1972-0298990-4**[6]**James V. Ralston,*Note on a paper of Kreiss*, Comm. Pure Appl. Math.**24**(1971), no. 6, 759–762. MR**0606239**

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DOI:
https://doi.org/10.1090/S0025-5718-1972-0341888-3

Article copyright:
© Copyright 1972
American Mathematical Society