On quasi-consistent integration by Nordsieck methods

DOI10.1016/j.cam.2008.07.038zbMath1163.65058OpenAlexW2168204527MaRDI QIDQ1004018

G. Yu. Kulikov

Publication date: 2 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.07.038

zbMATH Keywords

numerical examplesadaptivitylocal error estimationautomatic global error controldouble quasi-consistencyimplicitly extended Nordsieck formulasNordsieck-Adams-Moulton methodsquasi-consistent Nordsieck methods

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) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (11)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation ⋮ Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations ⋮ Explicit and implicit error inhibiting schemes with post-processing ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems ⋮ Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control ⋮ Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes ⋮ Local and global error estimation and control within explicit two-step peer triples ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• DIFSUB
• GEAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constant coefficient linear multistep methods with step density control
• Nordsieck representation of DIMSIMs
• Superconvergent explicit two-step peer methods
• The best parameterization for parametric interpolation
• Linearly-implicit two-step methods and their implementation in Nordsieck form
• Time-step selection algorithms: adaptivity, control, and signal processing
• Nordsieck methods on nonuniform grids: stability and order reduction phenomenon
• Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems
• Solving Ordinary Differential Equations I
• On Numerical Integration of Ordinary Differential Equations
• Equivalent Forms of Multistep Formulas
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
• Analysis of Fixed-Stepsize Methods
• Consistency of Nordsieck Methods
• Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
• On implicit extrapolation methods for ordinary differential equations
• Explicit, Time Reversible, Adaptive Step Size Control
• Local and global error estimation in Nordsieck methods

This page was built for publication: On quasi-consistent integration by Nordsieck methods