Global error estimation and control in linearly-implicit parallel two-step peer W-methods

DOI10.1016/j.cam.2011.08.006zbMath1269.65075OpenAlexW2077925666MaRDI QIDQ654736

G. Yu. Kulikov, Rüdiger Weiner

Publication date: 21 December 2011

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.2011.08.006

zbMATH Keywords

algorithmnumerical examplesautomatic global error controllinearly-implicit parallel peer W-methodslocal and global error estimationsstiff

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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) Numerical methods for stiff equations (65L04)

Related Items (16)

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 ⋮ High-order accurate continuous-discrete extended Kalman filter for chemical engineering ⋮ 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 ⋮ Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed ⋮ Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations ⋮ A new approach to estimating a numerical solution in the error embedded correction framework ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems ⋮ 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 ⋮ Estimating the State in Stiff Continuous-Time Stochastic Systems within Extended Kalman Filtering ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• RODAS

Cites Work

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