Previous article On Difference Approximations to Hyperbolic Differential Equations over Long Time IntervalsBertil GustafssonBertil Gustafssonhttps://doi.org/10.1137/0706046PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Heinz-Otto Kreiss, On difference approximations of the dissipative type for hyperbolic differential equations, Comm. Pure Appl. Math., 17 (1964), 335–353 MR0166937 0279.35059 CrossrefISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] H.-O. Kreiss and , O. Widlund , Difference approximations for initial value problems for partial differential equations , Rep. , Department of Computer Sciences, Uppsala University , Sweden , 1967 Google Scholar[4] John Gary, A generalization of the Lax-Richtmyer theorem on finite difference schemes, SIAM J. Numer. Anal., 3 (1966), 467–473 10.1137/0703040 MR0205484 0151.21404 LinkGoogle Scholar[5] Heinz-Otto Kreiss, Über die Stabilitätsdefinition für Differenzengleichungen die partielle Differentialgleichungen approximieren, Nordisk Tidskr. Informations-Behandling, 2 (1962), 153–181 MR0165712 0109.34702 CrossrefGoogle Scholar[6] Olof B. Widlund, On the stability of parabolic difference schemes, Math. Comp., 19 (1965), 1–13 MR0170479 0125.07402 CrossrefISIGoogle Scholar Previous article FiguresRelatedReferencesCited ByDetails Stability and A-stability of dissipative difference scheme for strongly hyperbolic systemsJapan Journal of Industrial and Applied Mathematics, Vol. 18, No. 2 | 1 Jun 2001 Cross Ref On the behavior over long time intervals of finite difference and finite element approximations to first order hyperbolic systemsComputers & Mathematics with Applications, Vol. 11, No. 1-3 | 1 Jan 1985 Cross Ref Asymptotics of Numerical Methods for Nonlinear Evolution EquationsTrends in The Theory and Practice of Non-Linear Analysis, Proceedings of the VIth International Conference on Trends in the Theory and Practice of Non-Linear Analysis | 1 Jan 1985 Cross Ref Stability of pseudospectral and finite-difference methods for variable coefficient problemsMathematics of Computation, Vol. 37, No. 156 | 1 January 1981 Cross Ref Application of Fast Poisson Solvers to A-Stable Marching Procedures for Parabolic ProblemsB. L. BuzbeeSIAM Journal on Numerical Analysis, Vol. 14, No. 2 | 14 July 2006AbstractPDF (876 KB)A-Convergence of Finite Difference Approximations of Parabolic Initial-Boundary Value ProblemsE. GekelerSIAM Journal on Numerical Analysis, Vol. 12, No. 1 | 14 July 2006AbstractPDF (800 KB)The Backward Beam Equation: Two A-Stable Schemes for Parabolic ProblemsAlfred CarassoSIAM Journal on Numerical Analysis, Vol. 9, No. 3 | 14 July 2006AbstractPDF (2146 KB) Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis317-522 History Submitted:07 July 1968Accepted:24 February 1969Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706046Article page range:pp. 508-522ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics