Parallel defect control

DOI10.1007/BF01933179zbMath0743.65069MaRDI QIDQ1182619

W. H. Enright, Desmond J. Higham

Publication date: 28 June 1992

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

interpolationnumerical resultsparallel computationerror controlRunge-Kutta formulanon stiff problemsparallel defect control

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)

Related Items (12)

Parallel interpolation of high-order Runge-Kutta methods ⋮ A family of parallel Runge-Kutta pairs ⋮ A new family of multistep numerical integration methods based on Hermite interpolation ⋮ Parallel defect control ⋮ Parallel implementation of interpolants for Runge-Kutta pairs ⋮ Parallel methods for initial value problems ⋮ Fast convergence pirkn-type pc methods with adams-type predictors^∗ ⋮ Runge-Kutta research at Toronto ⋮ Optimal residuals and the Dahlquist test problem ⋮ Parallel block pc methods with rkn-type correctors and adams-type predictors^∗ ⋮ Parallel block predictor-corrector methods of Runge-Kutta type ⋮ RKN-type parallel block PC methods with Lagrange-type predictors

Uses Software

• nag
• NSDTST
• STDTST

Cites Work

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• Parallel defect control
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• A block 6(4) Runge-Kutta formula for nonstiff initial value problems
• Analysis of Error Control Strategies for Continuous Runge–Kutta Methods
• Initial Value Routines in the NAG Library
• Nonlinear Wave Groups in Deep Water
• Global Error Estimation in Adams PC-Codes
• Global Error versus Tolerance for Explicit Runge-Kutta Methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Block Runge-Kutta Methods on Parallel Computers
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• Highly continuous Runge-Kutta interpolants
• Interpolants for Runge-Kutta formulas
• Two FORTRAN packages for assessing initial value methods
• Runge-Kutta triples
• Robust Defect Control with Runge–Kutta Schemes
• Certain Equivalent Requirements of Approximate Solutions of $x' = f(t,x)$.

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