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8.2.6-PDEs: Crank-Nicolson Implicit Finite Divided Difference Method

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Jacob Bishop

Jacob Bishop

11 жыл бұрын

These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale.

Пікірлер: 18
@bachpham7848
@bachpham7848 9 жыл бұрын
don't mind timmy, you voice flows like the rivers of babylon. thanks for all these vids! my lecturer is unmotivated and presents the course content in the most vague and difficult way to grasp. cheers for these vids you've saved me
@MechanicalEI
@MechanicalEI 5 жыл бұрын
Jacob Bishop, Great Video. The illustration and example of the Crank-Nicolson Implicit FDE Method were perfectly supported by your explanation. Thanks for uploading!
@jaco1159
@jaco1159 5 жыл бұрын
Thank you, this was very well explained and clear.
@kvyi
@kvyi 10 жыл бұрын
@timmy, Thanks for the suggestion. I agree.
@trillerbearstein3984
@trillerbearstein3984 9 жыл бұрын
Just two small corrections: For the implicit and explicit formulas you should have dT/dt = fwd finite divided difference instead of dT/dx2 The last term in the averaged centered divided difference approximation for d2T/dx2 should be Ti-1^L+1 instead of Ti-1^L Great video!
@kvyi
@kvyi 9 жыл бұрын
You are correct. Thank you for pointing this out. I wanted to note this with annotations, but youtube doesn't interpret the math right, so...
@engrirfanmahmood
@engrirfanmahmood 9 жыл бұрын
Jacob Bishop and maybe instead of 2 in denominator for Time discretization approximation there should be delta t?
@kvyi
@kvyi 9 жыл бұрын
Irfan Mahmood Annotations added. Thanks.
@TusharSharmatushar13992
@TusharSharmatushar13992 8 жыл бұрын
Nicely explained, thnx :)
@VipinP7708A
@VipinP7708A 5 жыл бұрын
Hi @Jacob Bishop, just a clarification. So using an initial vector for x for the initial condition, we construct the B vecto (Ax=B) and solve the equation for the first time level. Then we use this solution to construct the B vector for the next time level. Am I correct?
@kinghj3809
@kinghj3809 6 жыл бұрын
Thank you sir for this series it's reaaly helpful .. but there is a little bit of mistak in the expression of the second derivitive of "x" .. in the left ..you forgot to put (L+1).. for the last term of expression
@timothymoindi
@timothymoindi 10 жыл бұрын
hey nice video, i would suggest maybe having a script so that it flows better thanks
@Running_into_summer
@Running_into_summer 10 ай бұрын
thanks for explanation
@mitarona450
@mitarona450 6 жыл бұрын
thank you so much
@gabrieldominicbaygan2280
@gabrieldominicbaygan2280 7 жыл бұрын
Does the Crank-Nicholson scheme always produce a tri-diagonal matrix?
@eskamobob8662
@eskamobob8662 7 жыл бұрын
yes. It was designed to do so (back in the late 1800s when matrix inversion was horrid to do)
@fffppp8762
@fffppp8762 5 жыл бұрын
where is starting point?
@mabedsalah9444
@mabedsalah9444 5 жыл бұрын
Je cherche PDf please
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