The parametric solution of underdetermined linear ODEs

The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclid’s algorithm, and thus an alternative to the special case of a Gr¨obner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclid’s algorithm and the new ‘dual version’ are compared and their complementary strengths are analyzed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible under http://lie.math.brocku.ca/crack/uode. Key words: control theory, non-commutative Gr¨obner Bases, differential Gr¨obner Bases, linear ordinary differential equations, underdetermined differential equations 2000 MSC:...

• Type: Journal
• Year: 2011
• Where: PCS
• Authors: Thomas Wolf
• Keywords: Algorithm, Gr¨obner Bases, Operations Research, Ordinary Differential Equations, PCS 2011