SciML / OrdinaryDiffEq.jl

OrdinaryDiffEq.jl OrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the ordinary differential equation solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl. Installation Assuming that you already have Julia correctly installed, it suffices to import OrdinaryDiffEq.jl in the standard way: API OrdinaryDiffEq.jl is part of the SciML common interface, but can be used independently of DifferentialEquations.jl. The only requirement is that the user passes an OrdinaryDiffEq.jl algorithm to . For example, we can solve the ODE tutorial from the docs using the algorithm: That example uses the out-of-place syntax , while the in-place syntax (more efficient for systems of equations) is shown in the Lorenz example: Very fast static array versions can be specifically compiled to the size of your model. For example: For "refined ODEs", like dynamical equations and s, refer to the DiffEqDocs. For example, the harmonic oscillator equations can be solved using symplectic methods. The harmonic oscillator is described by: $$\ddot{x} + \omega^2 x = 0$$ which is equivalent to the first-order system: $$\dot{x} = v$$ $$\dot{v} = -\omega^2 x$$ For more complex dynamical systems, such as the Hénon-Heiles potential, symplectic integrators preserve the structure of Hamiltonian dynamics. In DiffEqTutorials.jl we show how to solve these equations of motion: Other refined forms are IMEX and semi-linear ODEs (for exponential integrators). Available Solvers For the list of available solvers, please refer to the DifferentialEquations.jl ODE Solvers, Dynamical ODE Solvers, and the Split ODE Solvers pages.