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Validated Runge-Kutta Methods for Initial Value Problems


Validated numerical integration methods based on explicit or 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 talk. More precisely, an efficient solution to the challenge of making validated Runge-Kutta methods is presented. We also present a new interval contractor approach to solve implicit Runge-Kutta methods. We also propose, in this talk, to use interval analysis tools to compute Runge-Kutta coefficients, in particular, a solver based on guaranteed constraint programming. Moreover, with a global optimization process and a well chosen cost function, we propose a way to define some novel optimal Runge-Kutta methods.
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hal-01762196 , version 1 (09-04-2018)


  • HAL Id : hal-01762196 , version 1


Julien Alexandre Dit Sandretto. Validated Runge-Kutta Methods for Initial Value Problems. ANODE, Feb 2018, Auckland, New Zealand. ⟨hal-01762196⟩
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