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Reports (Research Report) Year : 2015

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

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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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Dates and versions

hal-01107685 , version 1 (23-01-2015)
hal-01107685 , version 2 (26-01-2015)
hal-01107685 , version 3 (27-01-2015)
hal-01107685 , version 4 (29-01-2015)
hal-01107685 , version 5 (10-02-2015)
hal-01107685 , version 6 (13-03-2015)

Identifiers

  • HAL Id : hal-01107685 , version 6

Cite

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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