High order algebraically stable Runge-Kutta methods

DOI10.1007/BF01932017zbMath0401.65049MaRDI QIDQ4185755

Kevin Burrage

Publication date: 1978

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

StabilityOrdinary Differential EquationsNumerical MethodsInitial Value ProblemsRunge Kutta Methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Related Items (13)

The order of B-convergence of algebraically stable Runge-Kutta methods ⋮ On the \(A_ 0\)-acceptability of rational approximations to the exponential function with only real poles ⋮ Stability analysis of additive Runge-Kutta methods for delay-integro-differential equations ⋮ The dichotomy of stiffness: Pragmatism versus theory ⋮ Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations ⋮ On implicity Runge-Kutta methods with a stability function having distinct real poles ⋮ Perturbed collocation and Runge-Kutta methods ⋮ Constructive characterization of Runge-Kutta methods that satisfy the M-condition ⋮ Quadrature formulas with positive weights ⋮ Order properties of symplectic Runge-Kutta-Nyström methods ⋮ Non-linear stability of a general class of differential equation methods ⋮ Convergence results for general linear methods on singular perturbation problems ⋮ Blended implementation of block implicit methods for ODEs

Cites Work

• A stability property of implicit Runge-Kutta methods
• A special family of Runge-Kutta methods for solving stiff differential equations
• Stability and efficiency properties of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods
• Implicit Runge-Kutta Processes

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