Grid-based approximation of partial differential equations in Julia

Fast, continuous interpolation of discrete datasets in Julia

Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs

A 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.

A Julia package for defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.

A Julia package to perform Bifurcation Analysis

Julia package for Gaussian quadrature

High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

Adaptive 1d numerical Gauss–Kronrod integration in Julia

:rocket: Julia package for orthogonal polynomial transforms :snowboarder:

Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

Fast jacobian computation through sparsity exploitation and matrix coloring

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

Financial market technical analysis & indicators in Julia

CEED Library: Code for Efficient Extensible Discretizations

Pure-Julia multidimensional h-adaptive integration

The Base interface of the SciML ecosystem

Library for finding the roots of a function using interval arithmetic

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

Roll a window over data; apply a function over the window.

This is a Julia package of nonlinear solvers. These codes are used in my book, Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia.

Fast low-rank matrix approximation in Julia

Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

Automatic dualization feature for MathOptInterface.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.

A fully `Distributions.jl`-compliant copula package

Package implementing common state-space routines.

Random matrices package for Julia

A Julia package to solve, simulate, and analyze nonlinear DSGE models.

Implementation of variational Bayes inference algorithms

A Julia interface to the Artelys Knitro solver

Generation of Sobol low-discrepancy sequence (LDS) for the Julia language

Fast, SIMD-accelerated extended-precision arithmetic for Julia

Julia Wrappers for the arpack-ng Fortran library

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Calculate rigorously the feasible region for a set of real-valued inequalities with Julia