Extended Prelle–Singer procedure and Darboux polynomial method: An unknown interconnection. (January 2020)

• Record Type: Journal Article
• Authors: Manoranjani, M.; Mohanasubha, R.; Chandrasekar, V.K.; Senthilvelan, M.
• Is Part Of: International journal of non-linear mechanics. Volume 118(2020)
• Publication Date: 2020-01
• Subjects: Nonlinear ordinary differential equations -- Prelle–Singer method -- Null forms -- Integrating factors -- Darboux polynomials; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.103284
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this work, we present a new systematic procedure to derive two integrals from a Darboux polynomial for the given second order nonlinear ordinary differential equation (ODE). We succeed it by exploring an interlink between Darboux polynomial (DP) and the extended Prelle–Singer procedure (PS) quantities, namely null forms and integrating factors. We demonstrate the interconnection with suitable examples. Highlights: We present a new systematic procedure to derive two integrals from a Darboux polynomial for the given second order nonlinear ordinary differential equation. An unknown interconnection that exists between Darboux Polynomials and the extended Prelle–Singer procedure is obtained. The procedure is demonstrated for three different examples which are very familiar in the literature.