The Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge–Kutta Formulas

DOI10.1137/0730074zbMath0787.65046OpenAlexW1968884350MaRDI QIDQ3142636

W. H. Enright

Publication date: 20 December 1993

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

Full work available at URL: https://doi.org/10.1137/0730074

zbMATH Keywords

numerical resultsRunge-Kutta methodserror controldefectinterpolantsnon-stiff problemscontinuous methods

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 (14)

Numerical solutions of coupled differential equations and initial values using Maple software ⋮ New interpolants for asymptotically correct defect control of BVODEs ⋮ The reliability/cost trade-off for a class of ODE solvers ⋮ Numerically optimal Runge-Kutta pairs with interpolants ⋮ Piecewise-linearized methods for initial-value problems ⋮ A mixed finite element for the Stokes problem using quadrilateral elements ⋮ Issues in the numerical solution of evolutionary delay differential equations ⋮ Interpolating Runge-Kutta methods for vanishing delay differential equations ⋮ Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay ⋮ An error term and uniqueness for Hermite-Birkhoff interpolation involving only function values and/or first derivative values ⋮ Assessing cellular automata based models using partial differential equations ⋮ Runge-Kutta research at Toronto ⋮ A new method for exact integration of some perturbed stiff linear systems of oscillatory type ⋮ Continuous numerical methods for ODEs with defect control

Uses Software

• NSDTST
• STDTST

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