title: The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.
abstract: The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included.
authors.affiliation: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii prospekt 35, Petergof, Saint-Petersburg, Russia. ekalinina69@gmail.com
authors.forename: Elizabeth A
authors.initials: EA
authors.lastname: Kalinina
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D007473:Ion Channels / Q000737:chemistry; D008564:Membrane Potentials; D008954:Models, Biological; D011381:Programming Languages; D015203:Reproducibility of Results
chemical_list: D007473:Ion Channels
keywords: Euler's method; Floating-point arithmetic; Optimal step size; Real-time systems; Rounding errors; System of ordinary differential equations