Complexity reduction of C-Algorithm

• Published in: Applied mathematics and computation Vol. 217; no. 17; pp. 7318 - 7323
• Main Authors: Bardet, Magali, Boussaada, Islam
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.05.2011; Elsevier
• Subjects: Algorithms; Classical Analysis and ODEs; Combinatorics; Combinatorics. Ordered structures; Complexity; Computation; Computer algebra; Designs and configurations; Dynamical Systems; Exact sciences and technology; Isochronous centers; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Planar systems; Polynomial Liénard type systems; Qualitative theory; Reduction; Sciences and techniques of general use; Urabe function; Planar systems; Qualitative theory; Ordinary differential equations; Isochronous centers; Computer algebra; Urabe function; Polynomial Liénard type systems; Polynomial; Polynomial Lienard type systems; Differential equation; Differential system; Algorithmics; Algorithm; Implementation; Numerical analysis; Applied mathematics; Algorithm complexity; planar systems; polynomial Liénard type systems; computer algebra; Qualitative Theory; isochronous centers
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2011.02.023

The C-Algorithm introduced in [5] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case. The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in [1,2] to find many new examples of isochronous centers for the Liénard type equation.