Upgrade the KS solver in JAX to 2nd order

The Exponential Time Differencing algorithm of order one applied to the Kuramoto-Sivashinsky equation quickly becomes unstable. Let's fix that by upgrading it to a Runge-Kutta-style second-order method. Here is the code: github.com/Ceyron/machine-lea...
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Timestamps:
00:00 1st order method quickly becomes unstable
00:44 Theory of the ETDRK2 method
02:30 Algorithmic steps
05:10 Implementation
09:14 New trajectory with new autoregressive timestepper
11:03 Plotting and Discussion
11:41 Outro

[@marcjovanibertran3551]

In the ETDRK2 Method, the second constant c_1 should be (c_0 - 1)/L^ instead of (c_1 - 1)/L^?

[@MachineLearningSimulation]

You are absolutely right. 👍
It should have only affected the theory part in the beginning. I fixed the file on GitHub: github.com/Ceyron/machine-learning-and-simulation/blob/main/english/fft_and_spectral_methods/ks_solver_etd_and_etdrk2_in_jax.ipynb