A nonlinear optimization approach to the construction of general linear methods of high order

DOI10.1016/S0377-0427(97)00039-3zbMath0879.65051MaRDI QIDQ1362409

Zdzisław Jackiewicz, John C. Butcher, Hans D. Mittelmann

Publication date: 11 December 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

A-stabilitydiagonally implicit multistage integration methodsL-stabilitygeneral linear 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)

Related Items (15)

Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs ⋮ A new approach to the construction of DIMSIMs of high order and stage order ⋮ Strong stability preserving transformed DIMSIMs ⋮ Construction of highly stable two-step W-methods for ordinary differential equations ⋮ Construction and implementation of general linear methods for ordinary differential equations: a review ⋮ Order conditions for general linear methods ⋮ Derivation of symmetric composition constants for symmetric integrators ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ Applications of doubly companion matrices ⋮ Variable stepsize SDIMSIMs for ordinary differential equations ⋮ A new class of efficient general linear methods for ordinary differential equations ⋮ Construction of two-step Runge-Kutta methods of high order of ordinary differential equations ⋮ Exploiting structure in the construction of DIMSIMs ⋮ EFFICIENT GENERAL LINEAR METHODS OF HIGH ORDER WITH INHERENT QUADRATIC STABILITY ⋮ Implementation of DIMSIMs for stiff differential systems

Uses Software

• ADIFOR
• RODAS
• NL2SOL
• nlr

Cites Work

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• Generalized Padé approximations to the exponential function
• Diagonally-implicit multi-stage integration methods
• Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
• Diagonally implicit general linear methods for ordinary differential equations
• Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations
• Nordsieck representation of DIMSIMs
• Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
• Solving Ordinary Differential Equations I
• An Adaptive Nonlinear Least-Squares Algorithm
• Self-Scaling Variable Metric Algorithms without Line Search for Unconstrained Minimization
• Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation of parameters in nonlinear regression models
• Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations

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