On symmetric Runge-Kutta methods of high order

DOI10.1007/BF02238798zbMath0724.65074OpenAlexW1561827849MaRDI QIDQ758136

Robert P. K. Chan

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238798

zbMATH Keywords

Lobatto quadratureimplicit Runge-Kutta methodssymmetric methodsalgebraic stabilityLobatto IIISW-transformation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Generalized symmetric Runge-Kutta methods, Efficient symplectic Runge-Kutta methods, Delay-dependent stability of symmetric Runge-Kutta methods for second order delay differential equations with three parameters, Implicit Runge–Kutta methods based on Radau quadrature formula, Stability of Symmetric Runge--Kutta Methods for Neutral Delay Integro-Differential Equations, Constructive characterization of Runge-Kutta methods that satisfy the M-condition, An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. II: Convergence results, A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods, Construction of Runge-Kutta type methods for solving ordinary differential equations, Characterizations and construction of Poisson/symplectic and symmetric multi-revolution implicit Runge-Kutta methods of high order, SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION, Implicit Runge–Kutta methods based on Lobatto quadrature formula, Symmetric integrators based on continuous-stage Runge-Kutta-Nyström methods for reversible systems, \(A\)-stability of implicit Runge-Kutta extrapolations, On symmetrizers for Gauss method, A class of symplectic partitioned Runge-Kutta methods

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic expansions of the global error of fixed-stepsize methods
• Reflected and transposed Runge-Kutta methods
• Sur la B-stabilité des méthodes de Runge-Kutta
• Asymptotic expansions for the error of discretization algorithms for non- linear functional equations
• Algebraically Stable and Implementable Runge-Kutta Methods of High Order
• The Concept of B-Convergence
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• A short proof on nonlinearA-stability
• A stability property of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods
• On Extrapolation Algorithms for Ordinary Initial Value Problems
• A-stable Runge-Kutta processes
• Implicit Runge-Kutta Processes