Validated Explicit and Implicit Runge-Kutta Methods

Abstract : The guaranteed solution of initial value problem of ordinary differential equations is well studied from interval analysis community. In the most of the cases Taylor models are used in this context. In contrast, in numerical analysis community other numerical integration methods, e.g., Runge-Kutta methods, are used. Indeed, these methods have very good stability properties and they can be applied on a wide variety of problems. We propose a new method to validate the solution of initial value problem of ordinary differential equations based on Runge-Kutta methods. The strength of our contribution is to adapt any explicit and implicit Runge-Kutta methods to make them guaranteed. We experimentally verify our approach against Vericomp benchmark.
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Submitted on : Wednesday, February 11, 2015 - 2:41:07 PM
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  • HAL Id : hal-01111240, version 2

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Alexandre Chapoutot, Julien Alexandre Dit Sandretto, Olivier Mullier. Validated Explicit and Implicit Runge-Kutta Methods. Small Workshop on Interval Methods, Jun 2015, Prague, Czech Republic. ⟨hal-01111240v2⟩

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