Runge–Kutta Methods for Ordinary Differential Equations

DOI10.1007/978-3-319-17689-5_2zbMath1330.65109OpenAlexW2283094679MaRDI QIDQ3462303

John C. Butcher

Publication date: 5 January 2016

Published in: Numerical Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-17689-5_2

zbMATH Keywords

Runge-Kutta methodsTaylor seriessurvey paperorder conditionseffective orderrooted treesB-seriesefficient implementationimplicit methodselementary differentialsorder barriersG-symplectic methodsstrong stability preserving methodssingly-implicit methodslow-order methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

A Monte Carlo method for backward stochastic differential equations with Hermite martingales, High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation

Cites Work

• Unnamed Item
• Unnamed Item
• The cohesiveness of G-symplectic methods
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Runge-Kutta schemes for Hamiltonian systems
• A generalization of singly-implicit Runge-Kutta methods
• Towards Efficient Runge–Kutta Methods for Stiff Systems
• Total-Variation-Diminishing Time Discretizations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Dealing with Parasitic Behaviour in G-Symplectic Integrators
• The Control of Parasitism in $G$-symplectic Methods
• On the Attainable Order of Runge-Kutta Methods
• Geometric Numerical Integration
• Coefficients for the study of Runge-Kutta integration processes
• An Algebraic Theory of Integration Methods
• Numerical Methods for Ordinary Differential Equations