# A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

Andreas Rauh; Michael Brill; Clemens Günther

International Journal of Applied Mathematics and Computer Science (2009)

- Volume: 19, Issue: 3, page 381-397
- ISSN: 1641-876X

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topAndreas Rauh, Michael Brill, and Clemens Günther. "A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 381-397. <http://eudml.org/doc/207943>.

@article{AndreasRauh2009,

abstract = {The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.},

author = {Andreas Rauh, Michael Brill, Clemens Günther},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {ordinary differential equations; differential-algebraic equations; VALENCIA-IVP; verified simulation; inverse control problems; ValEncIA-IVP},

language = {eng},

number = {3},

pages = {381-397},

title = {A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP},

url = {http://eudml.org/doc/207943},

volume = {19},

year = {2009},

}

TY - JOUR

AU - Andreas Rauh

AU - Michael Brill

AU - Clemens Günther

TI - A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

JO - International Journal of Applied Mathematics and Computer Science

PY - 2009

VL - 19

IS - 3

SP - 381

EP - 397

AB - The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.

LA - eng

KW - ordinary differential equations; differential-algebraic equations; VALENCIA-IVP; verified simulation; inverse control problems; ValEncIA-IVP

UR - http://eudml.org/doc/207943

ER -

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