Keywords
- Difference Scheme
- Difference Operator
- Solution Operator
- Difference Quotient
- Dissipative Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M.Y.T. Apelkrans. On difference schemes for hyperbolic equations with discontinuous initial values. Math. Comp. 22 (1968), 525–539.
Ph. Brenner. The Cauchy problem for symmetric hyperbolic systems in LP. Math. Scand. 19 (1966), 27–37.
Ph. Brenner and V. Thomée. Stability and convergence rates in LP for certain difference schemes. Math. Scand. To appear.
Ph. Brenner and V. Thomée. Estimates near discontinuities for some difference schemes. To appear.
M.L. Buchanan. A necessary and sufficient condition for stability of difference schemes for intial-value problems. J.Soc.Indust.Appl.Math. 11 (1963), 919–935.
R. Courant, K. Friedrichs and H. Lewy. Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100 (1928), 32–74.
A. Friedman. Partial differential equations of parabolic type. Prentice-Hall. Englewood Cliffs, New Jersey, 1964.
K. Friedrichs. Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954), 345–392.
I.M. Gelfand and G.E. Schilow. Verallgemeinerte Funktionen III. Deutscher Verlag der Wissenschaften, Berlin, 1964.
S.K. Godunov and V.S. Ryabenkii. Introduction to the theory of difference schemes. Interscience. New York, 1964.
G.W. Hedstrom. The near-stability of the Lax-Wendroff method. Numer. Math. 7 (1965), 73–77.
G.W. Hedstrom. Norms of powers of absolutely convergent Fourier series. Michigan Math. J. 13 (1966), 393–416.
G.W. Hedstrom. The rate of convergence of some difference schemes. SIAM J. Numer. Anal. 5 (1968), 363–406.
G.W. Hedstrom. The rate of convergence of difference schemes with constant coefficients. BIT 9 (1969), 1–17.
F. John. On integration of parabolic equations by difference methods. Comm. Pure Appl. Math. 5 (1952), 155–211.
H.O. Kreiss. Über Matrizen die beschränkte Halbgruppen erzeugen. Math. Scand. 7 (1959), 71–80.
H.O. Kreiss. Uber die Losung des Cauchy problems fur lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. Acta Math. 101 (1959), 179–199.
H.O. Kreiss. Über die Stabilitätsdefinition für Differenzengleichungen die partielle Differentialgleichungen approximieren. BIT 2(1962), 153–181.
H.O. Kreiss. Über sachgemasse Cauchyprobleme. Math. Scand. 13 (1963), 109–128.
H.O. Kreiss. On difference approximations of dissipative type for hyperbolic differential equations. Comm. Pure Appl. Math. 17(1964), 335–353.
H.O. Kreiss, V. Thomée and O.B. Widlund. Smoothing of initial data and rates of convergence for parabolic difference equations. Comm. Pure Appl. Math. To appear.
P.D. Lax and R.D. Richtmyer. Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9 (1956), 267–293.
P.D. Lax and B. Wendroff. Systems of conservation laws. Comm. Pure Appl. Math. 13 (1960), 217–237.
P.D. Lax and B. Wendroff. Difference schemes for hyperbolic equations with high order or accuracy. Comm. Pure Appl. Math. 17 (1964), 381–398.
J. Löfström. Besov spaces in theory of approximation. Ann. Math. Pure Appl. 85 (1970), 93–184.
G.G. O’Brien, M.A. Hyman and S. Kaplan. A study of the numerical solution of partial differential equations. J. Math. and Phys. 29(1951), 223–251.
J. Peetre and V. Thomée. On the rate of convergence for discrete initial-value problems. Math. Scand. 21 (1967), 159–176.
R.D. Richtmyer and K.W. Morton. Difference methods for initial-value problems. 2nd ed., Interscience, New York, 1967.
V.S. Ryabenkii and A.F. Fillipow. Über die Stabilitat von Differenzengleichungen. Deutscher Verlag der Wissenschaften, Berlin, 1960.
S.I. Serdjukova. A study of stability of explicit schemes with constant real coefficients. Ž. Vyčisl. Mat. i Mat. Fiz. 3 (1963), 365–370.
S.I. Serdjukova. On the stability in C of linear difference schemes with constant real coefficients. Ž. Vyčisl. Mat i Mat. Fiz. 6(1966), 477–486.
W.G. Strang. Polynomial approximation of Bernstein type. Trans. Amer. Math. Soc. 105 (1962), 525–535.
V. Thomée. Stability of difference schemes in the maximum-norm. J. Differential Equations 1 (1965), 273–292.
V. Thomée. On maximum-norm stable difference operators. Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), pp. 125–151. Academic Press. New York.
V. Thomée. Parabolic difference operators. Math. Scand. 19 (1966), 77–107.
V. Thomée. Stability theory for partial difference operators. SIAM Rev. 11 (1969), 152–195.
V. Thomée. On the rate of convergence of difference schemes for hyperbolic equations. Numerical Solution of Partial Differential Equations. (Proc. Sympos. Univ. Maryland, 1970). To appear.
O.B. Widlund. On the stability of parabolic difference schemes. Math. Comp. 19 (1965), 1–13.
O.B. Widlund. Stability of parabolic difference schemes in the maximumnorm. Numer. Math. 8 (1966), 186–202.
O.B. Widlund. On the rate of convergence for parabolic difference schemes, II. Comm. Pure Appl. Math. 23 (1970), 79–96.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1971 Springer-Verlag
About this paper
Cite this paper
Thomée, V. (1971). Topics in stability theory for partial difference operators. In: Morris, J.L. (eds) Symposium on the Theory of Numerical Analysis. Lecture Notes in Mathematics, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060343
Download citation
DOI: https://doi.org/10.1007/BFb0060343
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05422-1
Online ISBN: 978-3-540-36538-9
eBook Packages: Springer Book Archive
