One-step 9-stage Hermite-Birkhoff-Taylor ODE solver of order 10

DOI10.1007/s12190-008-0216-3zbMath1177.65104OpenAlexW2080216663MaRDI QIDQ1034975

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

Publication date: 9 November 2009

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

Full work available at URL: https://doi.org/10.1007/s12190-008-0216-3

zbMATH Keywords

stabilitycomparison of methodsnumerical resultsRunge-Kutta methodTaylor methodstepsize controlHermite-Birkhoff methodCPU timenumber of function evaluationsmaximum global errorgeneral linear method for non-stiff ODE'sVandermonde-type linear systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) 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 (2)

A new family of multistep numerical integration methods based on Hermite interpolation ⋮ One-step 9-stage Hermite-Birkhoff-Taylor DAE solver of order 10

Uses Software

• QUADPACK

Cites Work

• 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
• Solving Ordinary Differential Equations Using Taylor Series
• Error estimation in automatic quadrature routines
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
• Implicit Runge-Kutta Processes
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