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Which numerical results can you trust? The Lorenz system as a test case

Tue, 13 Oct 2026 00:00:00 +0000

A computational physics course talk, From the convection equations to a trustworthy numerical solution. The slides run in the browser: soundadam.github.io/lorenz63. Use the arrow keys to move through them and N for the speaker notes. The slides and notes are in Chinese; the plots, equations and live demos read the same in any language.

A paradox

Integrate the Lorenz equations (σ=10, ρ=28, β=8/3) with DOP853 from scipy.solve_ivp, same initial condition, once with rtol=1e-6 and once with rtol=1e-12. For the first ten time units the two trajectories agree closely. Then they come apart until they are as far apart as the attractor is wide.

For teams

Mon, 01 Jan 0001 00:00:00 +0000

Model access for the research groups and teams I work with, on a platform I operate.

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