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 | References | Similar Articles | Additional Information

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

**[1]**S. Osher, ``Systems of difference equations with general homogeneous boundary conditions,''*Trans. Amer. Math. Soc.*, v. 137, 1969, pp. 177-201. MR**0237982 (38:6259)****[2]**H. O. Kreiss, ``Stability theory for difference approximations for mixed initial boundary value problems. I,''*Math. Comp.*, v. 22, 1968, pp. 703-714. MR**0241010 (39:2355)****[3]**H. O. Kreiss, ``Difference approximations for the initial-boundary value problem for hyperbolic differential equations,'' in*Numerical Solutions of Nonlinear Differential Equations*(Proc. Adv. Sympos., Madison, Wis., 1966), Wiley, New York, 1966, pp. 141-166. MR**35**#5156. MR**0214305 (35:5156)****[4]**I. C. Gohberg & M. G. Krein, ``Systems of integral equations on a half line with kernels depending on the difference of arguments,''*Uspehi Mat. Nauk*, v. 13, 1958, no. 2 (80), pp. 3-72; English transl.,*Amer. Math. Soc. Transl.*, v. (2) 14, 1960, pp. 217-288. MR**21**#1506; MR**22**#3954. MR**0113114 (22:3954)****[5]**H. O. Kreiss, ``On difference approximations of the dissipative type for hyperbolic differential equations,''*Comm. Pure Appl. Math.*, v. 17, 1964, pp. 335-353. MR**29**#4210. MR**0166937 (29:4210)**

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

Article copyright:
© Copyright 1969
American Mathematical Society