DiffEqDevTools.jl
DifferentialEquations.jl
DiffEqDevTools.jl | DifferentialEquations.jl | |
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3 | 6 | |
46 | 2,756 | |
- | 0.7% | |
8.5 | 7.2 | |
2 days ago | 25 days ago | |
Julia | Julia | |
GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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DiffEqDevTools.jl
- How much useful are Runge-Kutta methods of order 9 and higher within double-precision arithmetic/floating point accuracy?
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Interpolant Coefficients for the BS5 Runge-Kutta method
In general for tableaus the place to look is https://github.com/SciML/DiffEqDevTools.jl/blob/master/src/ode_tableaus.jl which is 10,000 lines of coefficients that have been checked to pass convergence tests at the correct order of accuracy. This means that many typos in the literature are fixed there, so these days I don't go back to the original sources (given how many typos I found).
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Tutorials for Learning Runge-Kutta Methods with Julia?
And that's why you use a library. Not even most library writers follow this stuff closely enough to be updating for minute improvements to scalar coefficients in tableaus of numbers. But in Julia we validated 8,000 lines of code describing these coefficients in higher precision accuracy and did the tests to choose the most effective methods out of that list. RK4 is almost never efficient. And even non-stiff ODE solvers are getting algorithmic improvements in the 2000's.
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?
SimpleDiffEq.jl - Simple differential equation solvers in native Julia for 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
QMUL - Repository of code and notes for the MSc. in Maths at Queen Mary University of London
diffeqpy - Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
Fortran-Astrodynamics-Toolkit - A Modern Fortran Library for Astrodynamics 🚀
Gridap.jl - Grid-based approximation of partial differential equations in Julia
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
ApproxFun.jl - Julia package for function approximation
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.