This is the final project in Numerical Methods II taught by Leslie Greengard (very smart guy) in 2021 Spring at NYU.

This is the Matlab implemention of the ADI for 2d heat equaiton.

The main implementation is under the file ADI2.m

In order to show the error log-log plots and tables, you also need to download the files related to "error", which are orignally from Randy LeVeque's website. The correspoding textbook is called "Finite Difference Methods for Ordinary and Partial Differential Equations".

https://faculty.washington.edu/rjl/

The methematical derivation is in the .pdf file. The stability analysis for this 2d problem is out of the scope of this course. However, I also include a brief description of basic steps of Von Neumann Analysis to this multi-step 2d method. This part of the analysis can be found on Trefethen's website

https://people.maths.ox.ac.uk/trefethen/4all.pdf.

He came up with BMI formula in 2013! He also published paper with his first wife Anna!

Google Trefethen for more information!