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Article Dans Une Revue Optimization Methods and Software Année : 2018

Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation

Résumé

A novel approach to bound the local truncation error of explicit and implicit Runge-Kutta methods is presented. This approach takes its roots in the modern theory of Runge-Kutta methods, namely the order condition theorem, defined by John Butcher in the 60's. More precisely, our work is an instance, for Runge-Kutta methods, of the generic algorithm defined by Ferenc Bartha and Hans Munthe-Kaas in 2014 which computes B-series with automatic differentiation techniques. In particular, this specialised algorithm is combined with interval analysis tools to define validated numerical integration methods based on Runge-Kutta methods.
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Dates et versions

hal-01498372 , version 1 (29-03-2017)

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Olivier Mullier, Alexandre Chapoutot, Julien Alexandre Dit Sandretto. Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation. Optimization Methods and Software, 2018, ⟨10.1080/10556788.2018.1459620⟩. ⟨hal-01498372⟩
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