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.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "computer-science",
	3	+ "topics": [
	4	+ "scientific-computing"
	5	+ ],
	6	+ "type": "algorithm",
	7	+ "benchmark": {
	8	+ "task": "Solve a 240-point semi-discrete Burgers' equation to t = 5 faster than RK45",
	9	+ "metric": {
	10	+ "name": "Speed-up over the reference implementation (×)",
	11	+ "better": "higher"
	12	+ },
	13	+ "baseline": {
	14	+ "name": "Reference implementation",
	15	+ "score": 1
	16	+ }
	17	+ },
	18	+ "source": {
	19	+ "key": "algotune",
	20	+ "name": "AlgoTune",
	21	+ "url": "https://github.com/oripress/AlgoTune/tree/main/AlgoTuneTasks/pde_burgers1d",
	22	+ "id": "pde_burgers1d",
	23	+ "curator": "Ori Press and the AlgoTune contributors",
	24	+ "poser": "Ori Press et al. (AlgoTune)",
	25	+ "status": "open",
	26	+ "as_of": "2026-10-20",
	27	+ "catalog": "0521c19bbd38"
	28	+ }
	29	+}