SciML/OrdinaryDiffEq.jlPublic

NotificationsYou must be signed in to change notification settings
Fork238
Star614

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

License

View license

614 stars 238 forks Branches Tags Activity

Star

Notifications

You must be signed in to change notification settings

Branches Tags

Folders and files

Name		Name	Last commit message	Last commit date
Latest commit History 10,638 Commits
.buildkite		.buildkite
.github		.github
benchmark		benchmark
docs		docs
lib		lib
src		src
test		test
.JuliaFormatter.toml		.JuliaFormatter.toml
.codecov.yml		.codecov.yml
.gitignore		.gitignore
.typos.toml		.typos.toml
CITATION.bib		CITATION.bib
CONTRIBUTING.md		CONTRIBUTING.md
LICENSE.md		LICENSE.md
Project.toml		Project.toml
README.md		README.md

Repository files navigation

OrdinaryDiffEq.jl

OrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds theordinary differential equation solvers and utilities. While completely independentand usable on its own, users interested in using thisfunctionality should check outDifferentialEquations.jl.

Installation

Assuming that you already have Julia correctly installed, it suffices to importOrdinaryDiffEq.jl in the standard way:

import Pkg;Pkg.add("OrdinaryDiffEq");

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 tosolve. For example, we can solve theODE tutorial from the docs using theTsit5() algorithm:

using OrdinaryDiffEqf(u, p, t)=1.01* uu0=1/2tspan= (0.0,1.0)prob=ODEProblem(f, u0, tspan)sol=solve(prob,Tsit5(), reltol=1e-8, abstol=1e-8)using Plotsplot(sol, linewidth=5, title="Solution to the linear ODE with a thick line",    xaxis="Time (t)", yaxis="u(t) (in μm)", label="My Thick Line!")# legend=falseplot!(sol.t, t->0.5*exp(1.01t), lw=3, ls=:dash, label="True Solution!")

That example uses the out-of-place syntaxf(u,p,t), while the inplace syntax (more efficient for systems of equations) is shown in the Lorenz example:

using OrdinaryDiffEqfunctionlorenz!(du, u, p, t)    du[1]=10.0(u[2]- u[1])    du[2]= u[1]* (28.0- u[3])- u[2]    du[3]= u[1]* u[2]- (8/3)* u[3]endu0= [1.0;0.0;0.0]tspan= (0.0,100.0)prob=ODEProblem(lorenz!, u0, tspan)sol=solve(prob,Tsit5())using Plots;plot(sol, idxs= (1,2,3))

Very fast static array versions can be specifically compiled to the size of your model. For example:

using OrdinaryDiffEq, StaticArraysfunctionlorenz(u, p, t)    SA[10.0(u[2]- u[1]), u[1]* (28.0- u[3])- u[2], u[1]* u[2]- (8/3)* u[3]]endu0= SA[1.0;0.0;0.0]tspan= (0.0,100.0)prob=ODEProblem(lorenz, u0, tspan)sol=solve(prob,Tsit5())

For "refined ODEs", like dynamical equations andSecondOrderODEProblems, refer to theDiffEqDocs. For example, inDiffEqTutorials.jl we show how to solve equations of motion using symplectic methods:

functionHH_acceleration!(dv, v, u, p, t)    x, y= u    dx, dy= dv    dv[1]=-x-2x* y    dv[2]= y^2- y- x^2endinitial_positions= [0.0,0.1]initial_velocities= [0.5,0.0]prob=SecondOrderODEProblem(HH_acceleration!, initial_velocities, initial_positions, tspan)sol2=solve(prob,KahanLi8(), dt=1/10);