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TitleSimple forms of higher-order linear differential systems and their applications in computing regular solutions
Author(s) Carole El Bacha, M.A. Barkatou, Thomas Cluzeau
TypeArticle in Journal
AbstractWe propose a direct algorithm for computing regular formal solutions of a given higher-order linear differential system near a singular point. With such a system, we associate a matrix polynomial and we say that the system is simple if the determinant of this matrix polynomial does not identically vanish. In this case, we show that the algorithm developed in Barkatou et al. (2009) can be applied to compute a basis of the regular formal solutions space. Otherwise, we develop an algorithm which, given a non-simple system, computes an auxiliary simple one from which the regular formal solutions space of the original system can be recovered. We also give the arithmetic complexity of our algorithms.
KeywordsComputer algebra, Higher-order linear differential systems, Singularities, Regular formal solutions, Matrix polynomials
URL http://www.sciencedirect.com/science/article/pii/S0747717111000137
JournalJournal of Symbolic Computation
Pages633 - 658
Translation No
Refereed No