The Finite Difference Method (2D)

The Finite Difference Method for 2D linear differential equations

in which I introduced the finite difference method for solving 1D linear ODEs.

I show how a 2D problem which naturally leads to a 3D matrix can be reduced to a 1D problem leading to a 2D matrix.
Once the problem is expressed as a 2D matrix, it is almost trivial to solve.

[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.

[martinaguayo]

Cheers Dave, the visuals really helped solidify my understanding.

[dalejulson]

Dave, did you ever make the video for Neumann boundary conditions?

[Morbecknaga]

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.

[honoriodombo]

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