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$\begingroup$ Thank you for the answer! For the part 1, can I ask you to elaborate a bit more on the newton's method part? Specifically in the context of this problem, what is the function $F$ that you mention? $\endgroup$
– sap7889
Commented Jul 2 at 20:55
$\begingroup$ Move everything to one side then that expression as a function of the current time step $\phi^{n+1}$ is $F$ $\endgroup$
– whpowell96
Commented Jul 2 at 20:58

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