The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “A verified method for solving piecewise smooth initial value problems”

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

Andreas Rauh, Michael Brill, Clemens Günther (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

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...

Interval analysis for certified numerical solution of problems in robotics

Jean-Pierre Merlet (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical...

Introduction to the Maple Power Tool Intpakx

Krämer, Walter (2007)

Serdica Journal of Computing

Similarity:

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The Maple Power Tool intpakX [24] de nes Maple types for real intervals and complex disc intervals. On the level of basic operations, intpakX includes the four basic arithmetic operators, including extended interval division as an extra function. Furthermore, there are power, square, square root, logarithm and exponential functions, a set of standard...

A Solver for Complex-Valued Parametric Linear Systems

Popova, Evgenija, Kolev, Lyubomir, Krämer, Walter (2010)

Serdica Journal of Computing

Similarity:

This work reports on a new software for solving linear systems involving affine-linear dependencies between complex-valued interval parameters. We discuss the implementation of a parametric residual iteration for linear interval systems by advanced communication between the system Mathematica and the library C-XSC supporting rigorous complex interval arithmetic. An example of AC electrical circuit illustrates the use of the presented software. * This work was partly supported...

Set arithmetic and the enclosing problem in dynamics

Marian Mrozek, Piotr Zgliczyński (2000)

Annales Polonici Mathematici

Similarity:

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

Computing and Visualizing Solution Sets of Interval Linear Systems

Krämer, Walter (2007)

Serdica Journal of Computing

Similarity:

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients...

Uses of new sensitivity and DAE solving methods in SmartMOBILE for verified analysis of mechanical systems

Ekaterina Auer, Wolfram Luther (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SmartMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features...