OrdinaryDiffEq.jl
Latexify.jl
| OrdinaryDiffEq.jl | Latexify.jl | |
|---|---|---|
| 3 | 2 | |
| 498 | 531 | |
| 0.2% | - | |
| 9.6 | 6.9 | |
| 7 days ago | 6 days ago | |
| Julia | Julia | |
| GNU General Public License v3.0 or later | MIT License |
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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
Latexify.jl
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Converting Symbolics.jl Objects to SymPy.jl Objects
My current solution to this is to use Latexify.jl, great module name btw, to convert the objects to latex, then perform some dodgy string manipulation on the latex, specifically turning it into a form readable by the Python module latex2sympy2 which has a function latex2sympy which can properly convert it. I've written a function to_sympy() which properly converts the Num and Matrix{NUM} types:
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Don't be scared.. Math and Computing are friends..
That's funny, I just implemented that conversion for Latexify.jl: https://github.com/korsbo/Latexify.jl/pull/205
What are some alternatives?
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.
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
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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.
SciMLTutorials.jl - Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
LaTeXDatax.jl - Julia plugin for the datax LaTeX package
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
Symbolics.jl - Symbolic programming for the next generation of numerical software
StochasticDiffEq.jl - Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R