The effective order of singly-implicit Runge-Kutta methods

DOI10.1023/A:1019176422613zbMath0936.65089OpenAlexW130410985MaRDI QIDQ1805902

Philippe Chartier, John C. Butcher

Publication date: 25 May 2000

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1019176422613

zbMATH Keywords

error estimationeffective ordersingly-implicit Runge-Kutta methodsstepsize change

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (13)

A generalization of singly-implicit Runge-Kutta methods ⋮ Symplectic effective order methods ⋮ The efficiency of singly-implicit Runge-Kutta methods for stiff differential equations ⋮ Inverse maximal eigenvalues problems for Leslie and doubly Leslie matrices ⋮ Applications of doubly companion matrices ⋮ The Hilber–Hughes–Taylor-α (HHT-α) method compared with an implicit Runge–Kutta for second-order systems ⋮ An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems ⋮ An efficient implicit Runge-Kutta method for second order systems ⋮ Effective order of partitioned Runge-Kutta methods ⋮ Hyman's method revisited ⋮ Symplectic effective order numerical methods for separable Hamiltonian systems ⋮ Order and effective order ⋮ ESIRK methods and variable stepsize

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