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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the equation

**[1]**Avner Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0181836****[2]**Heinz-Otto Kreiss,*Stability theory for difference approximations of mixed initial boundary value problems. I*, Math. Comp.**22**(1968), 703–714. MR**241010**, https://doi.org/10.1090/S0025-5718-1968-0241010-7**[3]**S. J. Osher,*Maximum norm stability for parabolic difference schemes in half-space*, Hyperbolic equations and waves (Rencontres, Battelle Res. Inst., Seattle, Wash., 1968) Springer, Berlin, 1970, pp. 61–75. MR**0657803****[4]**Stanley Osher,*Systems of difference equations with general homogeneous boundary conditions*, Trans. Amer. Math. Soc.**137**(1969), 177–201. MR**237982**, https://doi.org/10.1090/S0002-9947-1969-0237982-4**[5]**Stanley Osher,*Mesh refinements for the heat equation*, SIAM J. Numer. Anal.**7**(1970), 199–205. MR**266451**, https://doi.org/10.1137/0707013**[6]**Gilbert Strang,*Wiener-Hopf difference equations*, J. Math. Mech.**13**(1964), 85–96. MR**0160335****[7]**Gilbert Strang,*Implicit difference methods for initial-boundary value problems*, J. Math. Anal. Appl.**16**(1966), 188–198. MR**205496**, https://doi.org/10.1016/0022-247X(66)90196-X**[8]**Olof B. Widlund,*Stability of parabolic difference schemes in the maximum norm*, Numer. Math.**8**(1966), 186–202. MR**196965**, https://doi.org/10.1007/BF02163187**[9]**Olof B. Widlund,*On the rate of convergence for parabolic difference schemes. I*, Numerical Solution of Field Problems in Continuum Physics (Proc. Sympos. Appl. Math., Durham, N.C., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 60–73. MR**0264867****[10]**Olof B. Widlund,*On the rate of convergence for parabolic difference schemes. I*, Numerical Solution of Field Problems in Continuum Physics (Proc. Sympos. Appl. Math., Durham, N.C., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 60–73. MR**0264867****[11]**J. M. Varah,*Maximum norm stability of difference approximations to the mixed initial boundary-value problem for the heat equation*, Math. Comp.**24**(1970), 31–44. MR**260215**, https://doi.org/10.1090/S0025-5718-1970-0260215-1**[12]**J. M. Varah,*Stability of difference approximations to the mixed initial boundary value problems for parabolic systems*, SIAM J. Numer. Anal.**8**(1971), 598–615. MR**300475**, https://doi.org/10.1137/0708057

Retrieve articles in *Mathematics of Computation*
with MSC:
65M10

Retrieve articles in all journals with MSC: 65M10

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