General Differential Equations Packages
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ODE.jl106Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.
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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
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Makhno.jl0Spectral element code implemented in Julia
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SingularIntegralEquations.jl62Julia package for solving singular integral equations
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MovcolN.jl0Moving collocation method to solve one dimensional partial differential equations
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HPFEM.jl1HP Finite elements in Julia
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RiemannHilbert.jl5A Julia package for solving Riemann–Hilbert problems
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DifferentialEquations.jl2841Multi-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.
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WiltonInts84.jl1Integrals of arbitrary powers of R over flat triangles
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GeometricIntegrators.jl46Geometric Numerical Integration in Julia
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EconPDEs.jl121Solve non-linear HJB equations.
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ParameterizedFunctions.jl77A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications
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DiffEqBase.jl309The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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DiffEqDevTools.jl46Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
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StochasticDiffEq.jl248Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
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OrdinaryDiffEq.jl533High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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DiffEqParamEstim.jl61Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions
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DiffEqProblemLibrary.jl55A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools
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DiffEqSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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DiffEqUncertainty.jl65Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
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SingularSpectrumAnalysis.jl63A package for performing Singular Spectrum Analysis (SSA) and time-series decomposition
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DiffEqCallbacks.jl94A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
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DelayDiffEq.jl59Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.
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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)
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DiffEqOperators.jl285Linear operators for discretizations of differential equations and scientific machine learning (SciML)
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DynamicalSystems.jl834Award winning software library for nonlinear dynamics and nonlinear timeseries analysis
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StateSpaceModels.jl271StateSpaceModels.jl is a Julia package for time-series analysis using state-space models.
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Kalman.jl75Flexible filtering and smoothing in Julia
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ReachabilityAnalysis.jl189Computing reachable states of dynamical systems in Julia
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ComponentArrays.jl288Arrays with arbitrarily nested named components.
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StructuralIdentifiability.jl110Fast and automatic structural identifiability software for ODE systems
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ODEFilters.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
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ProbNumDiffEq.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
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HighDimPDE.jl71A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality
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OperatorLearning.jl43No need to train, he's a smooth operator
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FractionalDiffEq.jl80Solve Fractional Differential Equations using high performance numerical methods
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MethodOfLines.jl157Automatic Finite Difference PDE solving with Julia SciML
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