Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control

DOI10.1016/j.apnum.2012.06.018zbMath1252.65117OpenAlexW2019564448MaRDI QIDQ450931

Rüdiger Weiner, G. Yu. Kulikov, Helmut Podhaisky

Publication date: 26 September 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.018

zbMATH Keywords

embedded formulaslocal error estimationautomatic global error controlvariable-stepsize doubly quasi-consistent numerical schemes

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (14)

Two-step peer methods with equation-dependent coefficients ⋮ Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements ⋮ 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 ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes ⋮ Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter ⋮ Adaptive ODE solvers in extended Kalman filtering algorithms ⋮ Local and global error estimation and control within explicit two-step peer triples ⋮ NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• Matlab
• ode23

Cites Work

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• Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
• Solving Ordinary Differential Equations I
• On Global Error Estimation and Control for Initial Value Problems
• Global error control in implicit parallel peer methods
• Analysis of Fixed-Stepsize Methods
• Consistency of Nordsieck Methods
• Local and global error estimation in Nordsieck methods

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