Mono-implicit Runge-Kutta schemes for the parallel solution of initial value ODEs

DOI10.1016/S0377-0427(98)00221-0zbMath0945.65077OpenAlexW1975351522WikidataQ126867874 ScholiaQ126867874MaRDI QIDQ1300768

P. H. Muir, David A. Voss

Publication date: 21 September 2000

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(98)00221-0

zbMATH Keywords

performancenumerical resultsNewton's methodA-stabilityL-stabilityimplicit Runge-Kutta methodsstiff initial value problems

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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) Complexity and performance of numerical algorithms (65Y20)

Related Items (6)

Polynomial Chaos Expansions for Stiff Random ODEs ⋮ Stein implicit Runge-Kutta methods with high stage order for large-scale ordinary differential equations ⋮ The Hilber–Hughes–Taylor-α (HHT-α) method compared with an implicit Runge–Kutta for second-order systems ⋮ An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems ⋮ An efficient implicit Runge-Kutta method for second order systems ⋮ A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations

Cites Work

• Unnamed Item
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• Parallel Runge-Kutta methods with real eigenvalues
• Efficient classes of Runge-Kutta methods for two-point boundary value problems
• A parallel DIRK method for stiff initial-value problems
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Efficient higher order implicit one-step methods for integration of stiff differential equations
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• A special family of Runge-Kutta methods for solving stiff differential equations
• Order Results for Mono-Implicit Runge–Kutta Methods
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form

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