General Differential Equations Packages

ODE.jl101Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

Sundials.jl188Julia 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

Makhno.jl0Spectral element code implemented in Julia

SingularIntegralEquations.jl57Julia package for solving singular integral equations

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

HPFEM.jl1HP Finite elements in Julia

RiemannHilbert.jl5A Julia package for solving Riemann–Hilbert problems

DifferentialEquations.jl2503Multilanguage 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.

WiltonInts84.jl0Integrals of arbitrary powers of R over flat triangles

GeometricIntegrators.jl42Geometric Numerical Integration in Julia

EconPDEs.jl91Solve forwardlooking PDEs (e.g. HJB equations).

ParameterizedFunctions.jl72A simple domainspecific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

DiffEqBase.jl243The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

DiffEqDevTools.jl43Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

StochasticDiffEq.jl200Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

OrdinaryDiffEq.jl425High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

DiffEqParamEstim.jl51Easy scientific machine learning (SciML) parameter estimation with prebuilt loss functions

DiffEqProblemLibrary.jl39A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

DiffEqSensitivity.jl248A 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.

DiffEqUncertainty.jl59Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

SingularSpectrumAnalysis.jl51A package for performing Singular Spectrum Analysis (SSA) and timeseries decomposition

DiffEqCallbacks.jl52A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

DelayDiffEq.jl46Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differentialalgebraic equations.

DiffEqNoiseProcess.jl55A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

DiffEqOperators.jl279Linear operators for discretizations of differential equations and scientific machine learning (SciML)

DynamicalSystems.jl725Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

StateSpaceModels.jl235StateSpaceModels.jl is a Julia package for timeseries analysis using statespace models.

Kalman.jl69Flexible filtering and smoothing in Julia

ReachabilityAnalysis.jl170Methods to compute sets of states reachable by dynamical systems

ComponentArrays.jl231Arrays with arbitrarily nested named components.

StructuralIdentifiability.jl63Fast and automatic structural identifiability software for ODE systems

ODEFilters.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

ProbNumDiffEq.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

HighDimPDE.jl60A Julia package that breaks down the curse of dimensionality in solving PDEs.

OperatorLearning.jl37No need to train, he's a smooth operator

FractionalDiffEq.jl62Solve Fractional Differential Equations using high performance numerical methods

MethodOfLines.jl118Automatic Finite Difference PDE solving with Julia SciML
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