Parallel methods for initial value problems
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Publication:686538
DOI10.1016/0168-9274(93)90037-RzbMath0781.65060OpenAlexW2074559083MaRDI QIDQ686538
Publication date: 10 October 1993
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0168-9274(93)90037-r
Nonlinear ordinary differential equations and systems (34A34) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Linear ordinary differential equations and systems (34A30) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05)
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Cites Work
- Unnamed Item
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- Parallelism across time in ODEs
- The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs
- Efficient block predictor-corrector methods with a small number of corrections
- Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods
- Remarks on Picard-Lindelöf iteration. II
- Linear acceleration of Picard-Lindelöf iteration
- A sixth order predictor-corrector method for periodic IVPs
- Parallel ODE-solvers with stepsize control
- Multi-grid dynamic iteration for parabolic equations
- Sets of convergence and stability regions
- On the \(A_ 0\)-acceptability of rational approximations to the exponential function with only real poles
- Treatment of some mathematical models describing long-range transport of air pollutants on vector processors
- Numerical treatment of large-scale air pollution models
- Remarks on Picard-Lindelöf iteration
- On implicity Runge-Kutta methods with a stability function having distinct real poles
- Parallel algorithms for initial-value problems for difference and differential equations
- A parallel block cyclic reduction algorithm for the fast solution of elliptic equations
- Numerical experiments with nonlinear multigrid waveform relaxation on a parallel processor
- The error behaviour of a general class of predictor-corrector methods
- Parallel defect control
- Optimally stable parallel predictors for Adams-Moulton correctors
- Parallel iteration of high-order Runge-Kutta methods with stepsize control
- On quadrature methods for highly oscillatory integrals and their implementation
- Convergence of Dynamic Iteration Methods for Initial Value Problems
- Iterated Runge–Kutta Methods on Parallel Computers
- On the Implementation of Singly Implicit Runge-Kutta Methods
- Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
- Multi-Splittings of Matrices and Parallel Solution of Linear Systems
- Parallel Solution of ODE’<scp>s</scp> by Multiblock Methods
- Order Properties of Implicit Multivalue Methods for Ordinary Differential Equations
- A Scheme for Fast Parallel Communication
- Embedded Diagonally Implicit Runge-Kutta Algorithms on Parallel Computers
- Block Runge-Kutta Methods on Parallel Computers
- On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
- The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer
- A stability property of implicit Runge-Kutta methods
- Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems
- Attainable order of rational approximations to the exponential function with only real poles
- A special family of Runge-Kutta methods for solving stiff differential equations
- Waveform Iteration and the Shifted Picard Splitting
- Contractivity of Waveform Relaxation Runge–Kutta Iterations and Related Limit Methods for Dissipative Systems in the Maximum Norm
- The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
- Parallel methods for integrating ordinary differential equations
- Parallel Methods for the Numerical Integration of Ordinary Differential Equations
- Block Implicit One-Step Methods
- The automatic solution of systems of ordinary differential equations by the method of Taylor series
- Some Computer Organizations and Their Effectiveness
- A Runge-Kutta for all Seasons