GabrielFollet
commented
5 months ago When computing the Ice growth we need to solve a ODE with initial values, here we can integrate the numerical method that we saw in MUDE ( Euler(forward/backward), numerical integrations schemes ( mainly ZOH, trapezoidal and Gauss( at least this was optional when i did the course)
But i think we also need to add some very useful/famous numerical ODE solvers, such as the RK- family, Predicto-Corrector-family (Milne, Adams - Moulton) [ might be good segue into ultra-stables/ stiff ODE) ( we would need to find a ODE related to some of the topics, that is stiff.
The last part may be a little bit out of the scope of MUDE, but considering that there isnt a proper "numerical-methods course", at least being aware of stiff equation could be potentially useuful.
Similar, for the Boundary problem ODE part, where we use finite difference we could introduce the 'shooting method' to transforme the BVP into IVP ( not related to ice, but yeah, could be cool for people to know about this technique)
1. The Function explore_data() plots the individual time series for each variable, we can clearly see some seasonality and could stationarized the data and plot the modified time-series. ( either new function or optional argument for the already function)
1.1 We could implement de-trending for [daily,weekly-monthly-seasonality-yearly] (harmonic), and replot.
1.2 We could also integrate this with the signal processing module, by ploting the spectrogram for the [daily,weekly-monthly-seasonality-yearly] intervals we could visually evaluate the stationarity assumption
1.3 Or in the context of ARMA/(auto)correlation, explore the use of running mean/ moving average as ' pseudo' lowband pass filter (explore how this chanes depending on the size of the window)