These videos are excellent and easy to follow and implement. Prof Owkes any reference text that you can recommend for these topics, especially the finite difference method
@prof.markowkes-montanastat3851
3 жыл бұрын
Numerical Methods for Engineers by Chapra is a good reference.
@elormdonkor2897
3 жыл бұрын
@@prof.markowkes-montanastat3851 THANK YOU
@jasonbowens8369
3 жыл бұрын
THANK YOU!!!!
@muhammadnurfirdaus6723
5 жыл бұрын
Greetings Sir I want to ask you about your boundary grid. Why you set for example (1,1), (2,1), (3,1), (4,1) as boundary condition instead of (1,0), (2,0), (3,0), (4,0) ? Hope I can get your feedback. Thanks
@prof.markowkes-montanastat3851
5 жыл бұрын
In MATLAB the indexing starts at 1. So using this notation is consistent with the code written in part 3 of this video series.
@muhammadnurfirdaus6723
5 жыл бұрын
@@prof.markowkes-montanastat3851 Thanks for your feedback Dr. Really appreciate it . TQSM
@muhammadnurfirdaus6723
5 жыл бұрын
@@prof.markowkes-montanastat3851 Dr, if I want to set (1,0), (2,0), (3,0), (4,0) as boundary grid, would it be possible?
@israelmoya7702
4 жыл бұрын
what if my boundary condition is a derivative. Should I just sit down and cry?
@prof.markowkes-montanastat3851
4 жыл бұрын
No, don't cry. You need to discretize the derivative using either a forward (left/bottom boundary) or backward (right/top) finite difference operator. Once discretized, you can think about how to write the resulting equation in the appropriate row in the matrix. E.g. for dp/dx=0 on the left side, you could write ( p_{i+1,j} - p_{i,j} )/dx=0 and simplify this to 1*p_{i,j} + (-1)*p_{i+1,j)=0 which results in a 1 on the main diagonal and a -1 on the diagonal to the right of the main diagonal and a 0 in the array on the RHS.
@israelmoya7702
4 жыл бұрын
@@prof.markowkes-montanastat3851 Thank you so much for replying. Honestly, I did not think my comment would be even read. I actually understand your explanation, so I guess I will complete my matrix tomorrow and try the code. Thank you again.
@prof.markowkes-montanastat3851
3 жыл бұрын
@Johnny Rocketstick You can use a forward or backward difference for the Neuman BCs. They will only be 1st-order accurate, but will provide a fine solution. You could use a 2-order, one-sided finite difference but I would only explore that after you get the 1st-order method working. Yes, if you have different dx and dy then the off-diagonals will be dx^2 or dy^2 if you have multipled the entire equation by dx^2*dy^2.
@fadoobaba
6 жыл бұрын
If dx does not equal dy, then there will be ratio of squares of dx/dy in far away columns.
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