2000/07/15 by E.S. Cheb-Terrab, E. S. Cheb-Terrab, T. Kolokolnikov +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #34G20 #FOS: Mathematics #FOS: Physical sciences #General Mathematics (math.GM) #Geophysics and Sensor Technology #Mathematical Physics (math-ph) #Numerical methods for differential equations #Optical Polarization and Ellipsometry #math-ph #math.GM #math.MP #msc:34G20
paper · pdf · doi:10.48550/arxiv.math-ph/0007023
13 pages. Submitted to European Journal of Applied Mathematics, July 2000. Related Maple programs are available at http://lie.uwaterloo.ca/odetools.htm
arxiv created 2000/07/15 · openalex publication_date 2000/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An algorithm for solving first order ODEs, by systematically determining symmetries of the form [ xi = F(x), eta = P(x) y + Q(x) ], where xi d/dx + eta d/dy is the symmetry generator - is presented. To these \it linear symmetries one can associate an ODE class which embraces all first order ODEs mappable into separable through linear transformations t = f(x), u = p(x) y + q(x). This single ODE class includes as members, for instance, 78% of the 552 solvable first order examples of Kamke's book. Concerning the solving of this class, a restriction on the algorithm being presented exists only in the case of Riccati type ODEs, for which linear symmetries \it always exist but the algorithm will succeed in finding them only partially.