Stability of parabolic difference approximations to certain mixed initial boundary value problems

Author:
Stanley Osher

Journal:
Math. Comp. **26** (1972), 13-39

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298990-4

MathSciNet review:
0298990

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the equation

**[1]**A. Friedman,*Partial Differential Equations of Parabolic Type*, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR**31**#6062. MR**0181836 (31:6062)****[2]**H.-O. Kreiss, ``Stability theory for difference approximations of mixed initial boundary value problems. I,''*Math. Comp.*, v. 22, 1968, pp. 703-714. MR**39**#2355. MR**0241010 (39:2355)****[3]**S. Osher, ``Maximum norm stability for parabolic difference schemes in half-space,'' in*Hyperbolic Equations and Waves*, Springer-Verlag, New York, 1969, pp. 61-75. MR**0657803 (58:31885)****[4]**S. Osher, ``Systems of difference equations with general homogeneous boundary conditions,''*Trans. Amer. Math. Soc.*, v. 137, 1969, pp. 177-201. MR**38**#6259. MR**0237982 (38:6259)****[5]**S. Osher, ``Mesh refinements for the heat equation,''*Sinum*, v. 7, 1970, pp. 199-205. MR**0266451 (42:1357)****[6]**G. Strang, ``Weiner-Hopf difference equations,''*J. Math. Mech.*, v. 13, 1964, pp. 85-96. MR**28**#3548. MR**0160335 (28:3548)****[7]**G. Strang, ``Implicit difference methods for initial boundary value problems,''*J. Math. Anal. Appl.*, v. 16, 1966, pp. 188-198. MR**34**#5323. MR**0205496 (34:5323)****[8]**O. B. Widlund, ``Stability of parabolic difference schemes in the maximum norm,''*Numer. Math.*, v. 8, 1966, pp. 186-202. MR**33**#5149. MR**0196965 (33:5149)****[9]**O. B. Widlund,*On the Rate of Convergence for Parabolic Difference Schemes*. I, SIAM-AMS Proceedings, vol. 2, Amer. Math. Soc., Providence, R. I., 1970, pp. 60-73. MR**0264867 (41:9458a)****[10]**O. B. Widlund,*On the Rate of Convergence for Parabolic Difference Schemes*. II,*Comm. Pure Appl. Math.*, v. 23, 1970, pp. 79-96. MR**0264868 (41:9458b)****[11]**J. M. Varah, ``Maximum norm stability of difference approximations to the mixed initial boundary-value problem for the heat equation,''*Math. Comp.*, v. 24, 1970, pp. 31-44. MR**41**#4843. MR**0260215 (41:4843)****[12]**J. M. Varah, ``Stability of difference approximations to the mixed initial boundary value problem for parabolic systems.'' (To appear.) MR**0300475 (45:9521)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298990-4

Keywords:
Stability,
difference methods,
parabolic,
initial boundary value problem

Article copyright:
© Copyright 1972
American Mathematical Society