Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge--Kutta Methods

DOI10.1137/S0036142994265802zbMath0891.65085MaRDI QIDQ3124049

S. N. Papakostas, Ch. Tsitouras

Publication date: 19 July 1998

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

zbMATH Keywords

stabilitynumerical exampleserror boundRunge-Kutta methodsNyström interpolantsBDF formulasmultivalue-multiderivative-multistage method

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) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

Runge-Kutta Pairs For Scalar Autonomous Initial Value Problems ⋮ A high-order explicit Runge-Kutta pair for initial value problems with oscillating solutions ⋮ Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs ⋮ Multivalue collocation methods free from order reduction ⋮ High-order zero-dissipative Runge-Kutta-Nyström methods

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