Global error estimation and the backward differentiation formulas

DOI10.1016/0096-3003(89)90119-7zbMath0675.65084OpenAlexW4255681810MaRDI QIDQ1122334

Robert D. Skeel

Publication date: 1989

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90119-7

zbMATH Keywords

global error controldifference correctionbackward differential formulasglobal error estimation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Roundoff error (65G50) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (12)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation ⋮ Local theory of extrapolation methods ⋮ 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 ⋮ 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 ⋮ 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 ⋮ 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

Uses Software

• NSDTST
• STDTST

Cites Work

• Thirteen ways to estimate global error
• Global Error Estimation in Adams PC-Codes
• A Metalgorithm for Adaptive Quadrature
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
• Two FORTRAN packages for assessing initial value methods
• Stability and Asymptotic Estimates in Nonautonomous Linear Differential Systems
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