The stability of difference approximations to a selfadjoint parabolic equation, under derivative boundary conditions
Authors:
C. M. Campbell and P. Keast
Journal:
Math. Comp. 22 (1968), 336346
MSC:
Primary 65.68
MathSciNet review:
0226889
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
Richard
S. Varga, Matrix iterative analysis, PrenticeHall, Inc.,
Englewood Cliffs, N.J., 1962. MR 0158502
(28 #1725)
 [2]
Milton
E. Rose, On the integration of nonlinear parabolic equations by
implicit difference methods, Quart. Appl. Math. 14
(1956), 237–248. MR 0085610
(19,65f)
 [3]
James
E. Gunn, The solution of elliptic difference equations by
semiexplicit iterative techniques, J. Soc. Indust. Appl. Math. Ser. B
Numer. Anal. 2 (1965), 24–45. MR 0179962
(31 #4199)
 [4]
A.
A. Samarskiĭ, Homogeneous difference schemes for nonlinear
equations of parabolic type, Z. Vyčisl. Mat. i Mat. Fiz.
2 (1962), 25–56 (Russian). MR 0196960
(33 #5144)
 [5]
I.
V. Frjazinov, On a difference approximation of the boundary
conditions for the third boundaryvalue problem, Ž.
Vyčisl. Mat. i Mat. Fiz. 4 (1964), 1106–1112
(Russian). MR
0176623 (31 #895)
 [6]
P.
Keast and A.
R. Mitchell, On the instability of the Crank Nicholson formula
under derivative boundary conditions, Comput. J. 9
(1966), 110–114. MR 0196953
(33 #5137)
 [7]
A.
N. Tihonov and A.
A. Samarskiĭ, Homogeneous difference schemes, Ž.
Vyčisl. Mat. i Mat. Fiz. 1 (1961), 5–63
(Russian). MR
0168127 (29 #5391)
 [8]
John
Gary, A generalization of the LaxRichtmyer theorem on finite
difference schemes, SIAM J. Numer. Anal. 3 (1966),
467–473. MR 0205484
(34 #5311)
 [9]
R.
Courant and D.
Hilbert, Methods of mathematical physics. Vol. I, Interscience
Publishers, Inc., New York, N.Y., 1953. MR 0065391
(16,426a)
 [10]
N.
S. Koshlyakov, M.
M. Smirnov, and E.
B. Gliner, Differential equations of mathematical physics,
Translated by Scripta Technica, Inc.; translation editor: Herbert J. Eagle,
NorthHolland Publishing Co., Amsterdam; Interscience Publishers John Wiley
and Sons New York, 1964. MR 0177179
(31 #1443)
 [1]
 R. S. Varga, Matrix Iterative Analysis, PrenticeHall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)
 [2]
 M. E. Rose, "On the integration of nonlinear parabolic equations by implicit difference methods," Quart. J. Appl. Math., v. 14, 1956, pp. 237248. MR 19, 65. MR 0085610 (19:65f)
 [3]
 J. F. Gunn, "The solution of elliptic difference equations by semiexplicit iterative techniques," J. SIAM Ser. B Numer. Anal., v. 2 1965, pp. 2445. MR 31 #4199. MR 0179962 (31:4199)
 [4]
 A. A. Samarskii, "Homogeneous difference schemes on nonlinear equations of parabolic type," Z. Vyčisl. Mat. i. Mat. Fiz., v. 2, 1962, pp. 2526. (Russian) MR 33 #5144. MR 0196960 (33:5144)
 [5]
 I. V. Fryazinov, "On a difference approximation of the boundary conditions for the third boundaryvalue problem," Ž. Vyčisl. Mat. i. Mat. Fiz., v. 4, 1964, pp. 11061112. (Russian) MR 31 #895. MR 0176623 (31:895)
 [6]
 P. Keast & A. R. Mitchell, "On the instability of the Crank Nicholson formula under derivative boundary conditions," Comput. J., v. 9, 1966, pp. 110114. MR 33 #5137. MR 0196953 (33:5137)
 [7]
 A. N. Tikhonov & A. A. Samarskii, "Homogeneous difference schemes," Ž. Vycisl. Mat. i. Mat. Fiz., v. 1, 1961, pp. 563. (Russian) MR 29 #5391. MR 0168127 (29:5391)
 [8]
 J. Gary, "A generalization of the LaxRichtmyer Theorem on finite difference schemes," SIAM J. Numer. Anal., v. 3, 1966, pp. 467473. MR 34 #5311. MR 0205484 (34:5311)
 [9]
 R. Courant & D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience, New York, 1953. MR 16, 426. MR 0065391 (16:426a)
 [10]
 N. S. Koshlyakov, M. M. Smirnov & E. B. Gliner, Differential Equations of Mathematical Physics, Amsterdam, NorthHolland; Interscience, New York, 1964. MR 31 #1443. MR 0177179 (31:1443)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196802268897
PII:
S 00255718(1968)02268897
Article copyright:
© Copyright 1968
American Mathematical Society
