Notebook Tutorials

📜 Extensive user guide, mostly based on step-by-step tutorials …

All tutorials are written in jupyter notebooks, that can be :

• read using the online documentation

• downloaded from the notebook folder and played with

📋 Table of content :

1. Basic usage : how to generate and use basic \(Q\)-coefficients and \(Q_\Delta\) approximations, through a step-by-step tutorial going from generic Runge-Kutta methods to SDC for simple problems.

2. Advanced tutorials : additional features or qmat to go deeper into time-integration (Node-to-Node formulation, use for non-linear problems, \(\phi\)-SDC, …)

3. Components usage : how to use the main utility modules, like qmat.lagrange, etc …

Base usage tutorial

📜 From Butcher Tables to Spectral Deferred Corrections …

• Step 1 : generate \(Q\)-coefficients
• Step 2 : build a Runge-Kutta type solver
• Step 3 : generate \(Q_\Delta\) coefficients
• Step 4 : build a Spectral Deferred Correction solver
• Step 5 : residuals of SDC sweeps

Advanced tutorials

📜 Going deeper into advanced time-integration topics …

• Advanced Tutorial 1 : Zero-to-Nodes (Z2N) and Node-to-Node (N2N) formulations for SDC
• Advanced Tutorial 2 : build a Runge-Kutta solver for non-linear ODEs
• Advanced Tutorial 3 : build a Spectral Deferred Correction solver for non-linear ODEs
• Advanced Tutorial 4 : build a Spectral Deferred Correction solver based on generic time-integrators

Components usage

📜 How to use the utility modules …

• Tutorial 1 : using the qmat.lagrange module
• Tutorial 2 : using the qmat.nodes module