A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11

DOI10.1016/j.cam.2009.12.015zbMath1188.65097OpenAlexW2015872765MaRDI QIDQ964941

Vladan Bozic, Rémi Vaillancourt, Emmanuel Kengne, Truong Nguyen-Ba

Publication date: 21 April 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.12.015

zbMATH Keywords

numerical resultsTaylor expansionHermite-Birkhoff methodgeneral linear methodinterval of absolute stabilityCPU timenumber of function evaluationscomparing ODE solversmaximum global errorVandermonde-type systemsDormand-Prince DP87DP87nonstiff first-order initial value problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical interpolation (65D05) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (2)

Strong-stability-preserving, Hermite-Birkhoff time-discretization based on \(k\) step methods and 8-stage explicit Runge-Kutta methods of order 5 and 4 ⋮ Direct numerical methods dedicated to second-order ordinary differential equations

Uses Software

• Taylor
• NSDTST
• STDTST

Cites Work

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• VSVO formulation of the Taylor method for the numerical solution of ODEs
• High order embedded Runge-Kutta formulae
• Validated solutions of initial value problems for ordinary differential equations
• Computing validated solutions of implicit differential equations
• Solving Ordinary Differential Equations I
• A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
• Solving Ordinary Differential Equations Using Taylor Series
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• Two FORTRAN packages for assessing initial value methods
• A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations
• Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
• Comparing Numerical Methods for Ordinary Differential Equations
• Implicit Runge-Kutta Processes

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