Portal de Periódicos da CAPES

Finite Difference Forms Containing Derivatives of Higher Order

1968; Society for Industrial and Applied Mathematics; Volume: 5; Issue: 4 Linguagem: Inglês

10.1137/0705056

1095-7170

Manfred Reimer,

Differential Equations and Numerical Methods

Previous article Next article Finite Difference Forms Containing Derivatives of Higher OrderManfred ReimerManfred Reimerhttps://doi.org/10.1137/0705056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Germund Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand., 4 (1956), 33–53 MR0080998 0071.11803 CrossrefGoogle Scholar[2] Germund Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Kungl. Tekn. Högsk. Handl. Stockholm. No., 130 (1959), 87– MR0102921 0085.33401 Google Scholar[3] P. J. Davis, Interpolation and Approximation, Blaisdell, New York, 1965 Google Scholar[4] B. Dejon, Stronger than uniform convergence of multistep difference methods, Numer. Math., 8 (1966), 29–41 10.1007/BF02165236 MR0192660 0135.38002 CrossrefISIGoogle Scholar[5] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar[6] Manfred Reimer, Zur Theorie der linearen Differenzenformeln, Math. Z., 95 (1967), 373–402 10.1007/BF01111689 MR0211612 0143.37902 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Unconditional stable methods for second order ordinary differential equationsInternational Journal of Computer Mathematics, Vol. 41, No. 3-4 Cross Ref Accuracy and stability of multistage multistep formulasNumerische Mathematik, Vol. 48, No. 1 Cross Ref Zur Konvergenz und Stabilität von direkten Mehrschritt-Verfahren für die spezielle Differentialgleichungy(m) =f(x, y)ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 65, No. 9 Cross Ref A proof of the first dahlquist barrier by order starsBIT, Vol. 24, No. 4 Cross Ref Dahlquist's first barrier for multistage multistep formulasBIT, Vol. 24, No. 4 Cross Ref Stability of explicit time discretizations for solving initial value problemsNumerische Mathematik, Vol. 37, No. 1 Cross Ref The Construction of Finite Difference Approximations to Ordinary Differential EquationsEusebius J. Doedel14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 15, No. 3AbstractPDF (1755 KB)Arithmetic tests forA-stability,A[α]-stability, and stiff-stabilityBIT, Vol. 18, No. 1 Cross Ref On the stability regions of multistep multiderivative methods27 August 2006 Cross Ref Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Formu xy =f(x, y, u, u x ,u y )Computing, Vol. 18, No. 2 Cross Ref Multistep methods using higher derivatives and damping at infinity1 January 1977 | Mathematics of Computation, Vol. 31, No. 137 Cross Ref Note onA-stability of multistep multiderivative methodsBIT, Vol. 16, No. 1 Cross Ref An algebraic approach toA-stable linear multistep-multiderivative integration formulasBIT, Vol. 14, No. 4 Cross Ref Volume 5, Issue 4| 1968SIAM Journal on Numerical Analysis History Submitted:06 February 1968Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705056Article page range:pp. 725-738ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics