Error estimation and control for ODEs

From MaRDI portal
Publication:617058

DOI10.1007/BF02728979zbMath1203.65122OpenAlexW4230610617MaRDI QIDQ617058

Lawrence F. Shampine

Publication date: 20 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02728979




Related Items (29)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methodsOptimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methodsAn adaptive step size controller for iterative implicit methodsDynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusionVariable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equationsHigh-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equationsEfficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methodsA new family of multistep numerical integration methods based on Hermite interpolationImplicit-Runge-Kutta-based methods for fast, precise, and scalable uncertainty propagationAsynchronous discrete event schemes for PDEsOptimal parameters for numerical solvers of PDEsWeak variable step-size schemes for stochastic differential equations based on controlling conditional momentsAdaptive step size controllers based on Runge-Kutta and linear-neighbor methods for solving the non-stationary heat conduction equationEfficient adaptive stochastic collocation strategies for advection-diffusion problems with uncertain inputsA comparison of three error indicators for adaptive high-order large eddy simulationBoosting the accuracy of finite difference schemes via optimal time step selection and non-iterative defect correctionNested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equationsA new approach to estimating a numerical solution in the error embedded correction frameworkDiscontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flowOptimization of \(\mathrm{CO}_2\) vibrational kinetics modeling in the full state-to-state approachLocal and global error estimation and control within explicit two-step peer triplesNIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurementsFully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integrationFlexible Nonhomogeneous Markov Models for Panel Observed DataAdaptive step-size selection for state-space probabilistic differential equation solversA Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal AlgorithmSpace-time adaptive multiresolution methods for hyperbolic conservation laws: Applications to compressible Euler equationsA Variable Stepsize, Variable Order Family of Low ComplexityA Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations


Uses Software


Cites Work


This page was built for publication: Error estimation and control for ODEs