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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.

1# Project rules
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3This benchmark was brought here from [AlgoTune](https://github.com/oripress/AlgoTune/tree/main/AlgoTuneTasks/pde_burgers1d). README.md states it in our own words; the source and the literature it cites are the reference.
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5- 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.
6- 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.
7- Cite what you build on, and credit AlgoTune when you report a result.
8- 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.
9- Negative results stay on their routes; say what failed in `## Next`.