Validated Solution of Initial Value Problem for Ordinary Differential Equations based on Explicit and Implicit Runge-Kutta Schemes

Abstract : We present in this report our tool based on Ibex library which provides an innovative and generic pro- cedure to simulate an ordinary differential equation with any Runge-Kutta scheme (explicit or implicit). Our validated approach is based on the classical two steps integration: the Picard-Lindelöf operator to enclose all the solutions on a one step, and the computation of the approximated solution and its Local Troncature Error. This latter is computed with a generic and elegant approach using interval arithmetic and Fréchêt derivatives. We perform a strong experimentation through many numerical experiments coming from three different benchmarks and the results are shown and compared with competition.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01107685
Contributor : Alexandre Chapoutot <>
Submitted on : Friday, March 13, 2015 - 11:19:31 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:05 AM
Long-term archiving on : Sunday, September 13, 2015 - 9:31:14 PM

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  • HAL Id : hal-01107685, version 6

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Julien Alexandre Dit Sandretto, Alexandre Chapoutot. Validated Solution of Initial Value Problem for Ordinary Differential Equations based on Explicit and Implicit Runge-Kutta Schemes. [Research Report] ENSTA ParisTech. 2015. ⟨hal-01107685v6⟩

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