2014/08/25 by V. E. Adler, V. É. Adler · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Algebra over a field #Algorithm #Applied mathematics #Differential equation #Differential operator #Geometry #Lattice (music) #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Operator (biology) #Order (exchange) #Pure mathematics #Recursion (computer science) #Symmetry (geometry) #nlin.SI
paper · pdf · doi:10.1016/j.jsc.2015.05.008
published as Journal of Symbolic Computations 2016, Volume 74, pp 125-139 · 22 pages
arxiv created 2014/08/25 · openalex publication_date 2015/06/14 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A generalized summation by parts algorithm is presented for solving of difference equations of the form Tm(y)-a[u]y=b[u] where T denotes the shift uj→ uj+1. Solvability of such type of equations with respect to coefficients of formal symmetry (or formal recursion operator) provides a convenient integrability test for evolutionary differential-difference equations u,t=f(u-m,…,um). The algorithm is implemented in \em Mathematica.