The Finite Difference Method (2D)

[@wandongkim]

Hi Dave, I am a student whose major is numerical analysis. Thank you for the video. Your explanation is so clear and cool. At 5:27, we converted a 5 by 5 grid to a row vector; the ordered number of the last element of the row vector seems to be 24, not 25 because it began with 0.

[@rustyelectron]

Hi Dave, thanks for these videos. I am relearning calculus for the past few weeks and hope to make it to differential equations by the end of this month. Although I won't understand the content of this video now but i am pretty sure that i will love it when I do.

[@martinaguayo8649]

Cheers Dave, the visuals really helped solidify my understanding.

[@Morbecknaga1928]

Hello Dave! I have a question for you. I'm attempting to use the 2d Finite Difference Method that you describe in this video on a large 301x301 lat/lon grid. I've been referencing the Finite difference coefficient wiki page, and I'm trying to figure out whether the example shown at about 4:32 would be considered a 2nd derivative with 2nd order accuracy, or a 2nd derivative with 4th order accuracy. Based on the coefficients, I'm assuming it would be 2nd order accuracy, but I wanted to get your opinion.

[@zxqu9972]

great video

[@polarisp8983]

awesome!

[@honoriodombo7584]

hello Dave, why we made the I = n+Nm? for n,m

[@DavesSpace]

Hi, we do this substitution so that all the gridpoints can be expressed using a single index instead of two indices. The choice of n + Nm is arbitrary but follows a logical pattern of stacking the columns on top of one another. By having a single index, the NxM equations with NxM grid points can be expressed in a single matrix of size NM x NM. Without doing this substitution you would need to use the equivalent of a three dimensional matrix to solve the equations.