Multi-implicit peer two-step W-methods for parallel time integration

DOI10.1007/s10543-005-2635-yzbMath1079.65082OpenAlexW1972865204MaRDI QIDQ2568622

Rüdiger Weiner, Bernhard A. Schmitt, Helmut Podhaisky

Publication date: 18 October 2005

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-2635-y

zbMATH Keywords

stabilitynumerical examplesparallel computationsuperconvergencecollocationstepsize controlKrylov methodsstiff ODEstiff initial value problemspeer W-methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (29)

IMEX peer methods for fast-wave-slow-wave problems ⋮ Superconvergent explicit two-step peer methods ⋮ Parallel start for explicit parallel two-step peer methods ⋮ Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements ⋮ Discrete adjoint implicit peer methods in optimal control ⋮ Two-step peer methods with continuous output ⋮ Efficient A-stable peer two-step methods ⋮ A class of implicit peer methods for stiff systems ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Explicit two-step peer methods ⋮ On algebraic stability of general linear methods and peer methods ⋮ Global error estimation and control in linearly-implicit parallel two-step peer W-methods ⋮ Linearly implicit GARK schemes ⋮ Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter ⋮ Superconvergent IMEX peer methods ⋮ Reprint of: Peer methods with improved embedded sensitivities for parameter-dependent ODEs ⋮ Adaptive ODE solvers in extended Kalman filtering algorithms ⋮ NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements ⋮ Rosenbrock-type `peer' two-step methods ⋮ Implicit parallel peer methods for stiff initial value problems ⋮ Implicit peer methods for large stiff ODE systems ⋮ High-order linearly implicit two-step peer - finite element methods for time-dependent PDEs ⋮ Parameter optimization for explicit parallel peer two-step methods ⋮ Adapted explicit two-step peer methods ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• RKC
• ROWMAP

Cites Work

• Lower bounds for the condition number of Vandermonde matrices
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• RKC: An explicit solver for parabolic PDEs
• Parallel `peer' two-step W-methods and their application to MOL-systems.
• Blended implementation of block implicit methods for ODEs
• Implicit parallel peer methods for stiff initial value problems
• Parallel half-block methods for initial value problems
• Parallel iteration of the extended backward differentiation formulas
• Parallel Two-Step W-Methods with Peer Variables
• General linear methods for stiff differential equations
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