Stability of difference approximations of dissipative type for mixed initial-boundary value problems. I

Author:
Stanley Osher

Journal:
Math. Comp. **23** (1969), 335-340

MSC:
Primary 65.67

DOI:
https://doi.org/10.1090/S0025-5718-1969-0246530-8

MathSciNet review:
0246530

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Abstract: H. O. Kreiss, [2], has recently extended the stability theory of difference approximations to include the hyperbolic system

**[1]**Stanley Osher,*Systems of difference equations with general homogeneous boundary conditions*, Trans. Amer. Math. Soc.**137**(1969), 177–201. MR**0237982**, https://doi.org/10.1090/S0002-9947-1969-0237982-4**[2]**Heinz-Otto Kreiss,*Stability theory for difference approximations of mixed initial boundary value problems. I*, Math. Comp.**22**(1968), 703–714. MR**0241010**, https://doi.org/10.1090/S0025-5718-1968-0241010-7**[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]**I. C. Gohberg and M. G. Kreĭn,*Systems of integral equations on a half line with kernels depending on the difference of arguments*, Amer. Math. Soc. Transl. (2)**14**(1960), 217–287. MR**0113114****[5]**Heinz-Otto Kreiss,*On difference approximations of the dissipative type for hyperbolic differential equations*, Comm. Pure Appl. Math.**17**(1964), 335–353. MR**0166937**, https://doi.org/10.1002/cpa.3160170306

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0246530-8

Article copyright:
© Copyright 1969
American Mathematical Society