patrick-kidger / patrick-kidger/diffrax
Even better Implicit Runge--Kutta methods
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refactor
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- Python
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Description
There's a few things we could do to tidy up their implementation even further. Most of these are primarily considered in the FIRK case, so it might need some thinking to generalise them to the general implicit case.
- Iterate closer to zero. See (8.1) of Hairer & Wanner.
- Smarter stage-value predictors using interpolation. See (8.5') of Hairer & Wanner.
- Transform linear problems into Hessenberg form. See (8.15) of Hairer & Wanner.
- Stiff error estimators: adjust the error estimators of implicit solvers to depend on the implicit problems being solved. See (8.19) and (8.20) of Hairer & Wanner.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Locate the existing implicit Runge–Kutta implementation and first understand how the FIRK and general implicit cases are structured. Read the cited Hairer & Wanner sections (8.1, 8.5', 8.15, 8.19, and 8.20), then determine which improvements can be scoped and tested independently. Done would require agreed behavior and validation for the selected solver improvements.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- python
- Domain
- backend
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100