How Effective is the ADI Method for Solving PDEs with Non-Constant Source Terms?

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The discussion centers around a MATLAB code related to the Alternating Direction Implicit (ADI) method for solving partial differential equations (PDEs). A user seeks recommendations for books, papers, or equations that address the inclusion of the F(x,y,t) term in the finite difference method, noting that the reference material they have been using, "The Finite Difference Method in PDE" by Mitchell, inadequately covers this aspect. The user emphasizes the importance of accessing additional resources, specifically lecture notes, to enhance their understanding of the topic.
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The code can be seen here:
http://www4.ncsu.edu/~zhilin/TEACHING/MA584/MATLAB/ADI/adi.m

If you can refere me to a book, paper, equation I would appreciate it, I have been following The Finite Difference Method in PDE from Mitchell but the methods briefly outlined there don't consider the F(x,y,t) term.
 
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