numericalanalysis

Numerical Algebra

JuliaAlgebra

SciML

SciML/SciMLDocs

Julia:

All you need is the following organization (My Idol Prof. Christopher Rackauckas):

SciML Open Source Scientific Machine Learning

Including agent based models JuliaDynamics

BioJulia

nathanaelbosch/ProbNumDiffEq.jl: Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

PerezHz/TaylorIntegration.jl: ODE integration using Taylor's method, and more, in Julia

gideonsimpson/BasicMD.jl: A collection of basic routines for Molecular Dynamics simulations implemented in Julia

Probablistic Numerical Methods:

Julia:

nathanaelbosch/ProbNumDiffEq.jl: Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

Python:

ProbNum — probnum 0.1 documentation

C++:

odeint

LLNL/sundials: Official development repository for SUNDIALS - a SUite of Nonlinear and DIfferential/ALgebraic equation Solvers. Pull requests are welcome for bug fixes and minor changes.

3.7.1. Partial differential equation

Partial Differential Equation (PDE) Solvers Overview · SciML

SurveyJuliaPDE/SurveyofPDEPackages: Survey of the packages of the Julia ecosystem for solving partial differential equations

SciML/DiffEqOperators.jl: Linear operators for discretizations of differential equations and scientific machine learning (SciML)

vavrines/Kinetic.jl: Universal modeling and simulation of fluid dynamics upon machine learning

Gridap

kailaix/AdFem.jl: Innovative, efficient, and computational-graph-based finite element simulator for inverse modeling

SciML/ExponentialUtilities.jl: Utility functions for exponential integrators for the SciML scientific machine learning ecosystem

goodtrixi-framework/Trixi.jl: Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia

JuliaIBM

ranocha/SummationByPartsOperators.jl: A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.

Ferrite-FEM/Ferrite.jl: Finite element toolbox for Julia

JuliaFEM

pseudospectralFourierFlows/FourierFlows.jl: Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains

Python：

DedalusProject/dedalus: A flexible framework for solving PDEs with modern spectral methods.

FEniCS Project

Integral Differential Equation

TSGut/SparseVolterraExamples.jl: A number of examples built on the method described in https://arxiv.org/abs/2005.06081 for solving nonlinear and integro-differential Volterra equations

JoshKarpel/idesolver: A general-purpose numerical integro-differential equation solver

vitesempl/RK-IDE-Julia: Julia package for solving Differential Equations with Discrete and Distributed delays

3.7.2 Fractional Differential and Calculus

Julia

SciFracX

SciFracX/FractionalDiffEq.jl: FractionalDiffEq.jl: A Julia package aiming at solving Fractional Differential Equations using high performance numerical methods

SciFracX/FractionalSystems.jl: Fractional order modeling and analysis in Julia.

SciFracX/FractionalCalculus.jl: FractionalCalculus.jl: A Julia package for high performance, fast convergence and high precision numerical fractional calculus computing.

SciFracX/FractionalTransforms.jl: FractionalTransforms.jl: A Julia package aiming at providing fractional order transforms with high performance.

JuliaTurkuDataScience/FdeSolver.jl: FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.

3.10. Model Evaluation

3.10.1. Structure Idendification

Julia:

SciML/StructuralIdentifiability.jl

alexeyovchinnikov/SIAN-Julia: Implementation of SIAN in Julia

3.10.2. Global Sensitivity Anylysis

Julia:

lrennels/GlobalSensitivityAnalysis.jl: Julia implementations of global sensitivity analysis methods.

SciML/GlobalSensitivity.jl

SciML/DiffEqSensitivity.jl: A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, and more for ODEs, SDEs, DDEs, DAEs, etc.

Python:

SALib/SALib: Sensitivity Analysis Library in Python. Contains Sobol, Morris, FAST, and other methods.

R:

sensitivity

fast

sensobol