General Differential Equations Packages

DifferentialEquations.jl2841Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.

DynamicalSystems.jl834Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

OrdinaryDiffEq.jl533High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

DiffEqSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

DiffEqBase.jl309The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

ComponentArrays.jl288Arrays with arbitrarily nested named components.

DiffEqOperators.jl285Linear operators for discretizations of differential equations and scientific machine learning (SciML)

StateSpaceModels.jl271StateSpaceModels.jl is a Julia package for timeseries analysis using statespace models.

StochasticDiffEq.jl248Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Sundials.jl208Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

ReachabilityAnalysis.jl189Computing reachable states of dynamical systems in Julia

MethodOfLines.jl157Automatic Finite Difference PDE solving with Julia SciML

EconPDEs.jl121Solve nonlinear HJB equations.

ProbNumDiffEq.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

ODEFilters.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

StructuralIdentifiability.jl110Fast and automatic structural identifiability software for ODE systems

ODE.jl106Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

DiffEqCallbacks.jl94A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

FractionalDiffEq.jl80Solve Fractional Differential Equations using high performance numerical methods

ParameterizedFunctions.jl77A simple domainspecific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Kalman.jl75Flexible filtering and smoothing in Julia

HighDimPDE.jl71A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and FeynmanKac methods to solve highdimensional PDEs without the curse of dimensionality

DiffEqUncertainty.jl65Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

DiffEqNoiseProcess.jl63A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

SingularSpectrumAnalysis.jl63A package for performing Singular Spectrum Analysis (SSA) and timeseries decomposition

SingularIntegralEquations.jl62Julia package for solving singular integral equations

DiffEqParamEstim.jl61Easy scientific machine learning (SciML) parameter estimation with prebuilt loss functions

DelayDiffEq.jl59Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differentialalgebraic equations.

DiffEqProblemLibrary.jl55A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

GeometricIntegrators.jl46Geometric Numerical Integration in Julia

DiffEqDevTools.jl46Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

OperatorLearning.jl43No need to train, he's a smooth operator

RiemannHilbert.jl5A Julia package for solving Riemann–Hilbert problems

WiltonInts84.jl1Integrals of arbitrary powers of R over flat triangles

HPFEM.jl1HP Finite elements in Julia

Makhno.jl0Spectral element code implemented in Julia

MovcolN.jl0Moving collocation method to solve one dimensional partial differential equations
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