BoundaryValueDiffEq.jl
DifferentialEquations.jl
BoundaryValueDiffEq.jl | DifferentialEquations.jl | |
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1 | 6 | |
40 | 2,761 | |
- | 0.9% | |
9.3 | 7.2 | |
6 days ago | 6 days ago | |
Julia | Julia | |
GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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BoundaryValueDiffEq.jl
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Old programming language is suddenly getting more popular again
This isn't theoretical too, here's an actual user who opened an issue where their MWE was using quaternions:
https://github.com/SciML/BoundaryValueDiffEq.jl/issues/52
This is how I found out it worked in the differential equation solver: users were using it. The issue was unrelated (they didn't define enough boundary conditions), so it's quite cool that it was useful to someone. It turns out the quaternions have use cases in 3D rotations:
https://en.wikipedia.org/wiki/Gimbal_lock
which is where this all comes in. Anyways, it's always cool to learn from users what your own library supports! That's really a Julia treat.
DifferentialEquations.jl
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Startups are building with the Julia Programming Language
This lists some of its unique abilities:
https://docs.sciml.ai/DiffEqDocs/stable/
The routines are sufficiently generic, with regard to Julia’s type system, to allow the solvers to automatically compose with other packages and to seamlessly use types other than Numbers. For example, instead of handling just functions Number→Number, you can define your ODE in terms of quantities with physical dimensions, uncertainties, quaternions, etc., and it will just work (for example, propagating uncertainties correctly to the solution¹). Recent developments involve research into the automated selection of solution routines based on the properties of the ODE, something that seems really next-level to me.
[1] https://lwn.net/Articles/834571/
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From Common Lisp to Julia
https://github.com/SciML/DifferentialEquations.jl/issues/786. As you could see from the tweet, it's now at 0.1 seconds. That has been within one year.
Also, if you take a look at a tutorial, say the tutorial video from 2018,
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When is julia getting proper precompilation?
It's not faith, and it's not all from Julia itself. https://github.com/SciML/DifferentialEquations.jl/issues/785 should reduce compile times of what OP mentioned for example.
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Julia 1.7 has been released
Let's even put raw numbers to it. DifferentialEquations.jl usage has seen compile times drop from 22 seconds to 3 seconds over the last few months.
https://github.com/SciML/DifferentialEquations.jl/issues/786
- Suggest me a Good library for scientific computing in Julia with good support for multi-core CPUs and GPUs.
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DifferentialEquations compilation issue in Julia 1.6
https://github.com/SciML/DifferentialEquations.jl/issues/737 double posted, with the answer here. Please don't do that.
What are some alternatives?
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
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
diffeqpy - Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
Gridap.jl - Grid-based approximation of partial differential equations in Julia
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
ApproxFun.jl - Julia package for function approximation
fortran-lang.org - (deprecated) Fortran website
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
FFTW.jl - Julia bindings to the FFTW library for fast Fourier transforms
CUDA.jl - CUDA programming in Julia.