High Order Algebraically Stable Multistep Runge–Kutta Methods

DOI10.1137/0724009zbMath0611.65046OpenAlexW2064369834MaRDI QIDQ3750933

Kevin Burrage

Publication date: 1987

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0724009

zbMATH Keywords

nonlinear stabilityRunge-Kutta methodslinear multistep methodsGauss-LegendreB-stabilityalgebraic stabilityG- stabilityr-step s-stage multistep Runge-Kutta methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (18)

Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t)) ⋮ Local error estimation for multistep collocation methods ⋮ The dichotomy of stiffness: Pragmatism versus theory ⋮ Nonlinear stability and convergence of two-step Runge-Kutta methods for Volterra delay integro-differential equations ⋮ Efficiently implementable multivalue methods for solving stiff ordinary differential equations ⋮ Trigonometrically fitted multi-step Runge-Kutta methods for solving oscillatory initial value problems ⋮ Construction of algebraically stable dimsims ⋮ A general class of linear unconditionally energy stable schemes for the gradient flows ⋮ B-convergence of general linear methods for stiff problems. ⋮ Symplectic properties of multistep Runge-Kutta methods. ⋮ Generalized linear multistep methods for ordinary differential equations ⋮ Stability of multistep Runge-Kutta methods for systems of functional-differential and functional equations. ⋮ Equilibrium attractive properties of a class of multistep Runge-Kutta methods ⋮ Asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations ⋮ \(D\)-convergence of general linear methods for stiff delay differential equations ⋮ Algebraically stable general linear methods and the \(G\)-matrix ⋮ Superconvergence for Multistep Collocation ⋮ Stability and $B$-convergence properties of multistep Runge-Kutta methods

This page was built for publication: High Order Algebraically Stable Multistep Runge–Kutta Methods