Simplifying assumptions for the order of partitioned multivalue methods

DOI10.1007/BF01933639zbMath0477.65051OpenAlexW2083564289MaRDI QIDQ3935393

Kevin Burrage, Pamela Moss

Publication date: 1980

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01933639

zbMATH Keywords

orderRunge-Kutta methodButcher seriespartitioned multivalue methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

General linear method: A survey, Order and stability properties of explicit multivalue methods, Local error estimation for multistep collocation methods, The dichotomy of stiffness: Pragmatism versus theory, Efficiently implementable multivalue methods for solving stiff ordinary differential equations, The error behaviour of a general class of predictor-corrector methods, Construction of two-step Runge-Kutta methods of high order of ordinary differential equations, Superconvergence for Multistep Collocation, Asymptotic expansions of the global error of fixed-stepsize methods

Cites Work

• On the Butcher group and general multi-value methods
• The Solution of the order conditions for general linear methods
• Non-linear stability of a general class of differential equation methods
• On the implementation of implicit Runge-Kutta methods
• Runge-Kutta methods with a multiple real eigenvalue only
• A special family of Runge-Kutta methods for solving stiff differential equations
• Stability and efficiency properties of implicit Runge-Kutta methods
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• Implicit Runge-Kutta Processes