A linear-algebraic method to compute polynomial PDE conservation laws. (January 2022)

• Record Type: Journal Article
• Authors: Boreale, Michele; Collodi, Luisa
• Is Part Of: Journal of symbolic computation. Volume 108(2022)
• Page Start: 55
• Page End: 72
• Publication Date: 2022-01
• Subjects: PDEs -- Conservation laws -- Linear algebra -- Polynomials -- Gröbner bases; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.06.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a method to compute polynomial conservation laws for systems of partial differential equations (PDE s). The method only relies on linear algebraic computations and is complete, in the sense it can find a basis for all polynomial fluxes that yield conservation laws, up to a specified order of derivatives and degree. We compare our method to state-of-the-art algorithms based on the direct approach on a few PDE systems drawn from mathematical physics.