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Journal Articles Reliable Computing electronic edition Year : 2016

Validated Explicit and Implicit Runge-Kutta Methods

Abstract

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local truncation error of any Runge-Kutta methods is the main contribution of this article which pushes back the current state of the art. More precisely, an efficient solution to the challenge of making validated Runge-Kutta methods is presented based on the theory of John Butcher. We also present a new interval contractor approach to solve implicit Runge-Kutta methods. A complete experimentation based on Vericomp benchmark is described.
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Dates and versions

hal-01243053 , version 1 (14-12-2015)

Licence

Attribution - NonCommercial - NoDerivatives

Identifiers

  • HAL Id : hal-01243053 , version 1

Cite

Julien Alexandre Dit Sandretto, Alexandre Chapoutot. Validated Explicit and Implicit Runge-Kutta Methods. Reliable Computing electronic edition, 2016, Special issue devoted to material presented at SWIM 2015, 22. ⟨hal-01243053⟩
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