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

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SUMMARY

The ADI (Alternating Direction Implicit) method is effective for solving partial differential equations (PDEs) with non-constant source terms, as discussed in the forum. Users referenced the MATLAB implementation available at http://www4.ncsu.edu/~zhilin/TEACHING/MA584/MATLAB/ADI/adi.m. The limitations of The Finite Difference Method in PDEs by Mitchell were highlighted, specifically its inadequate treatment of the F(x,y,t) term. Participants emphasized the importance of accessing comprehensive lecture notes for deeper understanding.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with the Alternating Direction Implicit (ADI) method
  • Basic knowledge of MATLAB programming
  • Experience with finite difference methods
NEXT STEPS
  • Study the implementation details of the ADI method in MATLAB
  • Review advanced lecture notes on PDEs that cover non-constant source terms
  • Explore additional literature on finite difference methods beyond Mitchell's work
  • Investigate numerical stability and convergence criteria for the ADI method
USEFUL FOR

Mathematicians, numerical analysts, and engineers involved in computational fluid dynamics or any field requiring the solution of PDEs with variable source terms.

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...
 

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