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Dieci, Luca

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Sliding Motion in Discontinuous Differential Systems: Theory and a Computational Approach

2008-01-26 , Dieci, Luca , Lopez, Luciano

In this report, we have collected notes of work done during the Academic Year 2006-07, while the second author was in visit at Georgia Tech. Our main goals are the following: to reinterpret the 1st order theory of Filippov and to propose second author corrections to the theory; to provide a systematic, and non-ambiguous way to define the vector field on the intersection of several surfaces of discontinuity, consistent with Filippov's construction; to propose, and implement, numerical methods to approximate a trajectory of systems with discontinuous right-hand sides, and to illustrate their performance on a few examples.

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Orthonormal Integrators Based on Householder and Givens Transformations

2000 , Dieci, Luca , Van Vleck, Erik S.

We carry further our work [DV2] on orthonormal integrators based on Householder and Givens transformations. We propose new algorithms and pay particular attention to appropriate implementation of these techniques. We also present a suite of Fortran codes and provide numerical testing to show the efficiency and accuracy of our techniques.

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