OPTIMIZATION-BASED SEARCH FOR NORDSIECK METHODS OF HIGH ORDER WITH QUADRATIC STABILITY POLYNOMIALS

DOI10.3846/13926292.2012.685497zbMath1260.65063OpenAlexW2060608186MaRDI QIDQ4906380

Angelamaria Cardone, Hans D. Mittelmann, Zdzisław Jackiewicz

Publication date: 11 February 2013

Published in: Mathematical Modelling and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3846/13926292.2012.685497

zbMATH Keywords

numerical examplesquadratic stabilitygeneral linear methodsNordsieck methodsleast-squares minimization

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Error propagation for implicit-explicit general linear methods ⋮ Strong stability preserving transformed DIMSIMs ⋮ Stability analysis of ef Gaussian direct quadrature methods for Volterra integral equations ⋮ RK-stable second derivative multistage methods with strong stability preserving based on Taylor series conditions ⋮ Multistep collocation methods for Volterra integro-differential equations ⋮ Extrapolation-based implicit-explicit general linear methods ⋮ Order conditions for general linear methods ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS ⋮ EFFICIENT GENERAL LINEAR METHODS OF HIGH ORDER WITH INHERENT QUADRATIC STABILITY ⋮ Construction of highly stable implicit-explicit general linear methods

Uses Software

• PITCON
• NL2SOL
• HOMPACK