Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients

Moulay A. Barkatou (1)

1 DMI

Let (S) Y'=A(x)Y be a system of first order linear differential equations with rational function coefficients. A singular point x0 of (S) is called an apparent singularity if there is a basis of formal solutions of (S) which are holomorphic in a neighborhood of x0. In this talk we shall present a new algorithm which, given a system of the form (S), detects apparent singularities and constructs an equivalent system (S') with rational coefficients, such that every singularity of (S') is a singularity of (S) that is not apparent. Our method can, in particular, be applied to the companion system of any linear differential equation with arbitrary order n . We thus have an alternative method to the standard methods for removing apparent singularities of linear differential operators. We shall compare our method to the one designed for operators and we shall show some applications and examples of computation.

Moulay A. Barkatou. Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients. Second Workshop Differential Equations by Algebraic Methods, (DEAM2), Feb 2011, Linz, Austria. ⟨hal-00685035⟩