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I am in a numerical methods for PDE's class and have just been introduced to the ADI method. My teacher has given a general 2D heat equation to numerically compute using ADI with Crank-Nicolson and ADI with Peaceman-Rachford schemes. I understand what ADI is doing, I just don't know what the difference is between these two schemes when ADI is implemented is. I'm missing something here...

I have of course scoured the internet for papers/textbooks that will make me understand how they are different, but all I am getting out of my research is that the CN scheme allowed for ADI and thus, the PR scheme to develop. Basically I am understanding it as if you implement ADI with CN you have the PR scheme. Is that wrong? I then just keep seeing the steps of ADI (i.e. take half points, keep x fixed, keep y fixed etc.). What is different? Do you think the wording of the problem statement is incorrect (like, it should just be use 2D CN, and then use ADI with PR) or is there a distinct difference? Please, if you are familiar with this stuff I would appreciate a response!

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# Difference between Crank-Nicolson and Peaceman-Rachford Schemes with ADI

Can you offer guidance or do you also need help?

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