SciML/OrdinaryDiffEq.jl

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

What it solves

OrdinaryDiffEq.jl provides a comprehensive set of solvers and utilities for solving ordinary differential equations (ODEs). It allows users to define mathematical models of change over time and compute their future states based on initial conditions and parameters.

How it works

The library implements a variety of algorithms (such as Tsit5() and VelocityVerlet()) to numerically integrate ODEs. Users define an ODE problem using ODEProblem or SecondOrderODEProblem, specifying the function describing the system's dynamics, the initial state, and the time span. The library supports both out-of-place syntax for simplicity and in-place syntax for better performance in larger systems of equations.

Who it’s for

It is designed for scientists, engineers, and researchers who need to perform numerical integration of dynamical systems, ranging from simple linear ODEs to complex Hamiltonian dynamics and symplectic integrators.

Highlights

  • Diverse Solver Library: Includes a wide range of ODE solvers, including those for dynamical and split ODEs.
  • Performance Optimization: Supports in-place updates and specialized compilation for static arrays to maximize speed.
  • Specialized ODE Types: Handles second-order ODEs and refined forms like IMEX and semi-linear ODEs.
  • SciML Ecosystem: Part of the same common interface used by DifferentialEquations.jl.

Related

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    SciML/DiffEqFlux.jl

    A Julia package that integrates differential equation solvers into neural networks to enable the creation of physically informed scientific machine learning models.

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    SciML/diffeqpy

    A Python package that provides high-performance differential equation solvers by utilizing the DifferentialEquations.jl library from Julia.

  • Project
    SciML/DifferentialEquations.jl

    A high-performance numerical solver suite for a wide variety of differential equations, supporting scientific machine learning and GPU acceleration.

  • Project
    SciML/DiffEqGPU.jl

    A GPU acceleration library for differential equation solvers that enables high-performance solving of large ODE systems or massive ensembles of ODEs across multiple GPU hardware vendors.

  • Project
    SciML/DataDrivenDiffEq.jl

    A Julia package for data-driven structural estimation and identification of differential equations, allowing users to automatically discover mathematical models from data.