One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control

DOI10.1007/s11075-006-9043-5zbMath1109.65061OpenAlexW1983932402MaRDI QIDQ857860

Sergey K. Shindin, G. Yu. Kulikov

Publication date: 5 January 2007

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-006-9043-5

zbMATH Keywords

stabilityinitial value problemslocal error estimationglobal error estimationmultistep one-leg methods on nonuniform grids

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 (18)

Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction ⋮ Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation ⋮ New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations ⋮ Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow ⋮ Automatic step size and order control in implicit one-step extrapolation methods ⋮ Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations ⋮ Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control ⋮ Global error estimation and control in linearly-implicit parallel two-step peer W-methods ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems ⋮ One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives ⋮ Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna ⋮ Estimating the State in Stiff Continuous-Time Stochastic Systems within Extended Kalman Filtering ⋮ A Variable Stepsize, Variable Order Family of Low Complexity ⋮ Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations ⋮ Time-adaptive partitioned method for fluid-structure interaction problems with thick structures

Uses Software

• RODAS

Cites Work

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• Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems
• Stability of multistep-methods on variable grids
• A technique for controlling the global error in multistep methods
• Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems
• Stability of Two-Step Methods for Variable Integration Steps
• G-stability is equivalent toA-stability
• Solving Ordinary Differential Equations I
• On One-Leg Multistep Methods
• The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
• Contractive methods for stiff differential equations part I
• One-leg Integration of Ordinary Differential Equations with Global Error Control
• A special stability problem for linear multistep methods
• Computational Science and Its Applications – ICCSA 2004

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