104 research outputs found
On the Reduction of Singularly-Perturbed Linear Differential Systems
In this article, we recover singularly-perturbed linear differential systems
from their turning points and reduce the rank of the singularity in the
parameter to its minimal integer value. Our treatment is Moser-based; that is
to say it is based on the reduction criterion introduced for linear singular
differential systems by Moser. Such algorithms have proved their utility in the
symbolic resolution of the systems of linear functional equations, giving rise
to the package ISOLDE, as well as in the perturbed algebraic eigenvalue
problem. Our algorithm, implemented in the computer algebra system Maple, paves
the way for efficient symbolic resolution of singularly-perturbed linear
differential systems as well as further applications of Moser-based reduction
over bivariate (differential) fields.Comment: Keywords: Moser-based Reduction, Perturbed linear Differential
systems, turning points, Computer algebr
Formal Solutions of a Class of Pfaffian Systems in Two Variables
In this paper, we present an algorithm which computes a fundamental matrix of
formal solutions of completely integrable Pfaffian systems with normal
crossings in two variables, based on (Barkatou, 1997). A first step was set in
(Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the
approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a
complementary step, we associate to our problem a system of ordinary linear
singular differential equations from which the formal invariants can be
efficiently derived via the package ISOLDE, implemented in the computer algebra
system Maple.Comment: Keywords: Linear systems of partial differential equations, Pfaffian
systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal
for
Formal Solutions of Singularly Perturbed Linear Differential Systems
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer algebra system Maple
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