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), 336-346

MSC:
Primary 65.68

MathSciNet review:
0226889

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**[1]**Richard S. Varga,*Matrix iterative analysis*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0158502****[2]**Milton E. Rose,*On the integration of non-linear parabolic equations by implicit difference methods*, Quart. Appl. Math.**14**(1956), 237–248. MR**0085610****[3]**James E. Gunn,*The solution of elliptic difference equations by semi-explicit iterative techniques*, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.**2**(1965), 24–45. MR**0179962****[4]**A. A. Samarskiĭ,*Homogeneous difference schemes for non-linear equations of parabolic type*, Z. Vyčisl. Mat. i Mat. Fiz.**2**(1962), 25–56 (Russian). MR**0196960****[5]**I. V. Frjazinov,*On a difference approximation of the boundary conditions for the third boundary-value problem*, Ž. Vyčisl. Mat. i Mat. Fiz.**4**(1964), 1106–1112 (Russian). MR**0176623****[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****[7]**A. N. Tihonov and A. A. Samarskiĭ,*Homogeneous difference schemes*, Ž. Vyčisl. Mat. i Mat. Fiz.**1**(1961), 5–63 (Russian). MR**0168127****[8]**John Gary,*A generalization of the Lax-Richtmyer theorem on finite difference schemes*, SIAM J. Numer. Anal.**3**(1966), 467–473. MR**0205484****[9]**R. Courant and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[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, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley and Sons New York, 1964. MR**0177179**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0226889-7

Article copyright:
© Copyright 1968
American Mathematical Society