QMUL
DiffEqDevTools.jl
| QMUL | DiffEqDevTools.jl | |
|---|---|---|
| 1 | 3 | |
| 4 | 46 | |
| - | - | |
| 0.0 | 8.5 | |
| almost 3 years ago | 17 days ago | |
| Jupyter Notebook | Julia | |
| - | GNU General Public License v3.0 or later |
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QMUL
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.
What are some alternatives?
SimpleDiffEq.jl - Simple differential equation solvers in native Julia for scientific machine learning (SciML)
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
Fortran-Astrodynamics-Toolkit - A Modern Fortran Library for Astrodynamics 🚀
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.
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