Glashoff, K.; Kreth, H. Vorzeichenstabile Differenzenverfahren für parabolische Anfangsrandwertaufgaben. (German) Zbl 0447.65054 Numer. Math. 35, 343-354 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations 35K05 Heat equation 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 15B48 Positive matrices and their generalizations; cones of matrices 65N06 Finite difference methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs Keywords:parabolic initial-boundary value problems; structure preservation; one- step difference schemes; sign stability; totally non-negative matrices Citations:Zbl 0006.29804 PDFBibTeX XMLCite \textit{K. Glashoff} and \textit{H. Kreth}, Numer. Math. 35, 343--354 (1980; Zbl 0447.65054) Full Text: DOI EuDML References: [1] Forsythe, G.E., Wasow, W.R.: Finite difference methods for partial equations. New York-London-Sydney: John Wiley 1960 · Zbl 0099.11103 [2] Gantmacher, F.R., Krein, M.G.: Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme. Berlin: Akademie-Verlag 1960 · Zbl 0088.25103 [3] Gorenflo, R.: Conservative difference schemes for diffusion problems. Preprint No. 39, Fachbereich Mathematik der FU Berlin · Zbl 0377.65047 [4] Karlin, S.: Total positivity I, Stanford, Colifornia: Stanford University Press 1968 · Zbl 0219.47030 [5] Polya, G.: Qualitatives über Wärmeausgleich. Z. Angew. Math. Mech.13, 125-128 (1933) · Zbl 0006.29804 · doi:10.1002/zamm.19330130217 [6] Schoenberg, I.J.: Über variationsvermindernde lineare Transformationen. Math. Z.32, 321-328 (1930) · JFM 56.0106.06 · doi:10.1007/BF01194637 [7] Sturm, Ch.: Sur une classe d’Equations à differences partielles. J. Math. Pures Appl.1, 373-444 (1836) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.