A Contrast of Some Runge–Kutta Formula Pairs

DOI10.1137/0727076zbMath0717.65050OpenAlexW4238156705MaRDI QIDQ5748823

James H. Verner

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1137/0727076

zbMATH Keywords

embedded Runge-Kutta methodExplicit formulasRunge-Kutta formula pairssuccessive order of accuracy

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Numerically optimal Runge-Kutta pairs with interpolants ⋮ Runge-Kutta pairs of orders 9(8) for use in quadruple precision computations ⋮ Runge–Kutta pairs of orders 8(7) with extended stability regions for addressing linear inhomogeneous systems ⋮ Explicit Runge-Kutta pairs with lower stage-order ⋮ Some Nyström pairs for the general second-order initial-value problem ⋮ A contrast of direct and transformed Nyström pairs ⋮ Optimized explicit Runge-Kutta pair of orders \(9(8)\)

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