Runge–Kutta Defect Control Using Hermite–Birkhoff Interpolation

DOI10.1137/0912053zbMath0745.65051OpenAlexW1984588467MaRDI QIDQ3977641

Desmond J. Higham

Publication date: 25 June 1992

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0912053

zbMATH Keywords

algorithmnumerical testsRunge-Kutta methoddefect controlHermite-Birkhoff interpolationstepsize selection

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (11)

New interpolants for asymptotically correct defect control of BVODEs ⋮ The reliability/cost trade-off for a class of ODE solvers ⋮ Birkhoff Polynomial Basis ⋮ Error estimation and control for ODEs ⋮ Polynomial algebra for Birkhoff interpolants ⋮ Parallel implementation of interpolants for Runge-Kutta pairs ⋮ An error term and uniqueness for Hermite-Birkhoff interpolation involving only function values and/or first derivative values ⋮ Solving ODEs and DDEs with residual control ⋮ Runge-Kutta research at Toronto ⋮ Continuous numerical methods for ODEs with defect control ⋮ A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws

Uses Software

• NSDTST
• STDTST

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