The Parametric Solution of Underdetermined linear ODEs

Please always quote using this URN: urn:nbn:de:0297-zib-10693
  • 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 Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at

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Author:Thomas Wolf
Document Type:ZIB-Report
Tag:Crack; Euclid's algorithm; Reduce; computer algebra; linear ODEs; underdetermined systems
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Hxx Control problems [See also 49J15, 49K15, 93C15] / 34H05 Control problems [See also 49J15, 49K15, 93C15]
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Hq Ordinary differential equations
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.70.-c Computational techniques; simulations (for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics) / 02.70.Wz Symbolic computation (computer algebra)
Date of first Publication:2008/03/10
Series (Serial Number):ZIB-Report (08-15)
Published in:Appeared in: Programming and Computer Software, 37 (2011), Number 2, pp. 62-70