Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control

DOI10.1137/090764840zbMath1215.65125OpenAlexW2025034850MaRDI QIDQ2998005

Publication date: 17 May 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1bd417857afdac35ea42e9f1694e9b6bfef02f72

zbMATH Keywords

interpolation stability convergence consistency numerical experiments approximation peer methods automatic global error control doubly quasi-consistent numerical schemes embedded formula error estimation variable-stepsize implementation

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)

Strong stability preserving explicit peer methods for discontinuous Galerkin discretizations ⋮ Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Optimally zero stable explicit peer methods with variable nodes ⋮ 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 ⋮ 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 ⋮ Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed ⋮ Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control ⋮ 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 ⋮ Implicit peer methods for large stiff ODE systems ⋮ A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

Matlab

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