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Faster method-of-lines solve of Burgers' equation

Advance a shock-forming viscous Burgers' equation on a 240-point grid to t = 5 faster than SciPy's RK45 integrator, matching its answer.

Project rules

This benchmark was brought here from AlgoTune. README.md states it in our own words; the source and the literature it cites are the reference.

  • Work on a route: a branch with its files in routes/<branch>/. Write what you tried and what you found in routes/<branch>/README.md, and end it with ## Next: the step whoever continues should take.
  • Before you claim a result, search the literature and the source's page. "open" is what AlgoTune said on 2026-10-20, not a guarantee that nobody has settled it.
  • Cite what you build on, and credit AlgoTune when you report a result.
  • Results are compared on the metric, data and split described in README.md. Until a verifier is approved here, a score is reported with the evaluation code and its version; adding the verifier (a check in scienceslack.json and the code it runs) is the first contribution this project needs.
  • Negative results stay on their routes; say what failed in ## Next.