Depot des Theses - Algebraic methods solving matrix differential equations of arbitrary order

In this thesis, we develop new algebraic methods for solving an important class of systems of linear differential equations of arbitrary order. Such systems appear in many scientific disciplines such as chemistry, physics, mechanics and control theory.Firstly, we are interested in the local analysis of systems of linear ordinary differential equations near a singularity. We develop algorithms for the computation of their regular formal solutions. These algorithms are direct, i.e., do not reduce the system to another one of firstorder and larger size. Our approaches use properties of matrix polynomials whose determinant plays the same role as indicial polynomials in the scalar case. Then, we are interested in the study of the so-called k-simple forms of a linear differential system of first-order. These forms give information on the integer slopes of the Newton polygon of the system and allow the computation of the formal solutions without ramification. Our contribution is reflected in the development of a direct method for the calculation of k-simple forms.Secondly, we focus on systems of linear differential-algebraic equations. Such systems are composed of differential equations coupled with algebraic ones. We propose algorithms for decoupling them into a purely differential part and a purely algebraic one.Another contribution of the thesis is the study of the complexity and the implementation in Maple of the algorithms developed. Créé par EL BACHA Carole 3 oct. 2014 Version 0.1

Nature

Thèse de doctorat

Subjects

Disciplines Doctorat/Mathématiques et Applications

Rights

Source

Coverage

Created at

3 oct. 2014

Last modified at

3 oct. 2014

Format

PDF

Language

Author

EL BACHA Carole

Last Contributor

system

Contributors

system