This is a copy of a project I worked on in my PDE course. Its a work that is being revised and will be updated in the next two to three weeks with an analysis of the decomposition method applied to the Navier Stokes equations and complications that arise.
I plan to submit a copy of this to the next issue of the MHF-Zine, with the updated Navier Stokes analysis and adding a section or two on ODEs. I also plan to include another section which talks about the convergence of solutions in more detail (i.e. the conditions which expedite the rate of convergence as well as what spaces the convergence of solutions take place.)
Let me know what I can do to improve the quality of this work, if necessary.