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

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davat45
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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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big fail, just had to go up one level on the internet address find the lecture notes and read...