# SciML/DifferentialEquations.jl

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

Repository: https://github.com/SciML/DifferentialEquations.jl
Canonical: https://ross.abutalabs.com/products/differentialequationsjl
Homepage: https://docs.sciml.ai/DiffEqDocs/stable/
Language: Julia
License: NOASSERTION
License Family: other
Topics: differential-equations, differentialequations, julia, ode, sde, dae, dde, spde, stochastic-processes, stochastic-differential-equations, delay-differential-equations, differential-algebraic-equations, dynamical-systems, neural-differential-equations, r, python, scientific-machine-learning, sciml, numerical, scientific
Last push: 2026-08-23T20:58:41+00:00

## Health v2 (maintenance only)
Score: 95/100 (v2, computed 2026-09-03T02:20:16.233290+00:00)
- activity 99, release rhythm 87, longevity 100
- inputs: {"age_days": 3766, "days_push": 10, "days_rel": 10, "gap_med": 58.5, "n_releases_24m": 9}
- flags: no_license
- formula: round(0.45*activity + 0.35*rhythm + 0.20*longevity); archived -> min(score, 10)

## Adoption (not part of the score)
Stars 3151, forks 256 (observed 2026-08-28T04:07:46.171213+00:00)

## What it is
A Julia suite of high-performance numerical solvers for differential equations, covering ODEs, SDEs, DDEs, DAEs, RODEs, jumps, and (S)PDEs, usable from Julia, Python, and R. It also provides scientific machine learning (SciML) components such as neural differential equations and includes some of the fastest implementations of classic and research-grade algorithms.

## Use cases
- solve ordinary differential equations numerically
- simulate stochastic differential equations
- solve stiff ODE systems efficiently
- solve delay differential equations with history functions
- simulate differential-algebraic equations
- train neural differential equations for scientific machine learning
- simulate dynamical systems and Gillespie/Markov jump processes
- solve partial differential equations with finite difference or finite element methods

## When to choose
- you need fast, high-accuracy solvers for ODEs, SDEs, DAEs, DDEs, or PDEs in Julia
- you want automatic algorithm selection and state-of-the-art performance beyond classic C/Fortran codes
- you need stiff large-scale systems with specialized linear solvers
- you want scientific machine learning features like neural differential equations
- you need high-precision or HPC-optimized integrators

## When to avoid
- you need a simple one-off ODE solve in Python and prefer SciPy's familiar API
- you want symbolic/analytic solutions rather than numerical ones
- you cannot adopt the Julia ecosystem or its v8 breaking-change migration
- you only need a single equation type and prefer a lightweight specialized package

## Facets
- artifact type: library
- maturity: active
- function: simulation, math, machine-learning, data-science
- domain: mathematics, data-science, performance
- platform: python, cross-platform
- tags: differential-equations, ode, sde, dde, dae, pde, scientific-computing, sciml, numerical-solvers, neural-differential-equations, algorithms, julia

## Member repositories
- SciML/DifferentialEquations.jl (main) score 95

## Provenance
- Observed fields: from GitHub, fetched 2026-08-28T04:07:46.171213+00:00.
- Health v2: computed from the inputs above; adoption is never an input.
- Inferred fields (summary, facets, guidance): AI-extracted, prompt v1, taxonomy v1, on 2026-08-30T07:25:42.186375+00:00, confidence not recorded.
  - readme: https://github.com/SciML/DifferentialEquations.jl (fetched 2026-08-28T04:07:46.171213+00:00, sha a0c69c089451)
  - homepage: https://docs.sciml.ai/DiffEqDocs/stable/ (fetched 2026-08-29T09:40:28.209745+00:00, sha 90f13f0bbb77)
  - site_page: https://docs.sciml.ai/DiffEqDocs (fetched 2026-08-29T09:40:28.219916+00:00, sha 82260832e07c)
  - site_page: https://docs.sciml.ai/DiffEqDevDocs (fetched 2026-08-29T09:40:28.221697+00:00, sha db0de492634b)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/getting_started (fetched 2026-08-29T09:40:28.223335+00:00, sha a11db7041cb3)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/faster_ode_example (fetched 2026-08-29T09:40:28.225854+00:00, sha 062ff9a300a4)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/advanced_ode_example (fetched 2026-08-29T09:40:28.228443+00:00, sha 9bd3fdc67fd7)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example (fetched 2026-08-29T09:40:28.230503+00:00, sha 033126865aae)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/rode_example (fetched 2026-08-29T09:40:28.232340+00:00, sha 940becb8b696)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable/tutorials/dde_example (fetched 2026-08-29T09:40:28.233991+00:00, sha 41e5407eeeb0)
- Data as of 2026-08-30T08:39:29.467469+00:00.