OrdinaryDiffEq.jl
StochasticDiffEq.jl
| OrdinaryDiffEq.jl | StochasticDiffEq.jl | |
|---|---|---|
| 3 | 1 | |
| 498 | 234 | |
| 0.2% | 0.4% | |
| 9.6 | 7.8 | |
| 7 days ago | 3 days ago | |
| Julia | Julia | |
| GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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OrdinaryDiffEq.jl
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Modern Numerical Solving methods
There has been a lot of research in Runge Kutta methods in the last couple decades which resulted in all kind of specialized Runge Kutta methods. You have high order ones, RK methods for stiff problems, embedded RK methods which benefit from adaprive step size control, RK-Nystrom methods for second order Problems, symplectic RK methods which preserve energy (eg. hamiltonian) ando so on. If you are interested in the numerics and the use cases I highly recommend checking out the Julia Libary OrdinaryDiffEq (https://github.com/SciML/OrdinaryDiffEq.jl). If you look into the documentation you find A LOT of implemented RK methods for all kind of use cases.
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Why Fortran is a scientific powerhouse
Project.toml or Manifest.toml? Every package has Project.toml which specifies bounds (https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/Proje...). Every fully reproducible project has a Manifest that decrease the complete package state (https://github.com/SciML/SciMLBenchmarks.jl/blob/master/benc...).
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How do the Julia ODE solvers choose/select their initial steps? What formula do they use to estimate the appropriate initial step size?
Yes. If you want to see a robust version of the algorithm you can check out https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/initdt.jl
StochasticDiffEq.jl
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Writing unit tests in scientific computing
For stochastic processes you have to work a little bit more. However maybe the StochasticDiffEq.jl package can give some guiding there https://github.com/SciML/StochasticDiffEq.jl/tree/master/test
What are some alternatives?
Latexify.jl - Convert julia objects to LaTeX equations, arrays or other environments.
SciMLTutorials.jl - Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
auto-07p - AUTO is a publicly available software for continuation and bifurcation problems in ordinary differential equations originally written in 1980 and widely used in the dynamical systems community.
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
SciMLSensitivity.jl - 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.
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. [Moved to: https://github.com/SciML/SciMLSensitivity.jl]
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
DiffEqOperators.jl - Linear operators for discretizations of differential equations and scientific machine learning (SciML)
ModelingToolkit.jl - An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
DifferentialEquations.jl - Multi-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.