References
Aronson, D. G.: Linear parabolic differential equations containing a small parameter. J. Rat. Mech. and Anal.5, 1003–1004 (1956).
Courant, R., K. O. Friedrichs andH. Lewy: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann.100, 32–74 (1928).
Douglas Jr, J.: The application of stability analysis in the numerical solution of quasi-linear parabolic differential equations. Trans. Amer. Math. Soc.89, 484–518 (1958).
Friedrichs, K. O.: Symmetric hyperbolic linear differential equations. Comm. Pure and Appl. Math.7, 345–392 (1954).
Kreiss, H. O.: Über die Lösung des Cauchy-Problems für lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. Acta Math.101, 179–199 (1959).
Lax, P. D., andB. Wendroff: Systems of conservation laws. Comm. Pure and Appl. Math.13, 217–237 (1960).
—: The scope of the energy method. Bull. Amer. Math. Soc.66, no. 1, 32–35 (1960).
—: On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients. Comm. Pure and Appl. Math.14, 497–520 (1961).
Mood, A. M.: Introduction to the Theory of Statistics. New York: McGraw-Hill 1950.
Parter, S. V.: On the eigenvalues of certain generalizations of Toeplitz matrices. (In press.)
Richtmyer, R. D.: Difference Methods for Initial Value Problems, Interscience Publishers. New York 1957.
Strang, Gilbert: Trigonometric polynomials and difference methods of maximum accuracy. Jour. Math. and Physics,41, 147–154 (1962).
Author information
Authors and Affiliations
Additional information
Portions of this work were undertaken during the summers of 1960 and 1961 while the author was at the Los Alamos Scientific Laboratories and the Sandia Corp. respectively.
Rights and permissions
About this article
Cite this article
Parter, S.V. Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem. Numer. Math. 4, 277–292 (1962). https://doi.org/10.1007/BF01386319
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01386319