On the Stability of Finite Difference Matrices
K. W. Morton, Samuel Schechter · Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis · 1965
Previous article Next article On the Stability of Finite Difference MatricesK. W. Morton and S. SchechterK. W. Morton and S. Schechterhttps://doi.org/10.1137/0702010PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Mary Louise Buchanan, A necessary and sufficient condition for stability of difference schemes for initial value problems, J. Soc. Indust. Appl. Math., 11 (1963), 919–935 10.1137/0111067 MR0160324 (28:3537) 0221.65144 LinkISIGoogle Scholar[2] David H. Carlson and , Hans Schneider, Inertia theorems for matrices: the semidefinite case, J. Math. Anal. Appl., 6 (1963), 430–446 10.1016/0022-247X(63)90023-4 MR0148678 (26:6185) 0192.13402 CrossrefGoogle Scholar[3] Heinz-Otto Kreiss, Über Matrizen die beschränkte Halbgruppen erzeugen, Math. Scand., 7 (1959), 71–80 MR0110952 (22:1820) 0090.09801 CrossrefGoogle Scholar[4] Heinz-Otto Kreiss, Über die Stabilitätsdefinition für Differenzengleichungen die partielle Differentialgleichungen approximieren, Nordisk Tidskr. Informations-Behandling, 2 (1962), 153–181 MR0165712 (29:2992) 0109.34702 CrossrefGoogle Scholar[5] H. O. Kreiss, Über sachgemässe Cauehyprobleme für Systeme von linearen partiellen Differentialgleichungen, Kungl. Tekn. Högsk. Handl. Stockholm, 127 (1958), 1–30 0084.29801 Google Scholar[6] P. D. Lax and , R. D. Richtmyer, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math., 9 (1956), 267–293 MR0079204 (18,48c) 0072.08903 CrossrefISIGoogle Scholar[7] K. W. Morton, On a matrix theorem due to H. O. Kreiss, Comm. Pure Appl. Math., 17 (1964), 375–379 MR0170460 (30:698) 0146.13702 CrossrefISIGoogle Scholar[8] Olga Taussky, Matrices C with $C\sp{n}\rightarrow 0$, J. Algebra, 1 (1964), 5–10 10.1016/0021-8693(64)90003-1 MR0161865 (28:5069) 0126.02802 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy MethodDoron Levy and Eitan Tadmor4 August 2006 | SIAM Review, Vol. 40, No. 1AbstractPDF (856 KB)Stability Theory for Partial Difference OperatorsVidar Thomée18 July 2006 | SIAM Review, Vol. 11, No. 2AbstractPDF (3792 KB) Volume 2, Issue 1| 1965Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis History Submitted:23 November 1964Published online:03 August 2006 InformationCopyright © 1965 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0702010Article page range:pp. 119-128ISSN (print):0887-459XISSN (online):2168-3581Publisher:Society for Industrial and Applied Mathematics