8.2.1-PDEs: Finite Divided Difference for Elliptic PDEs with Irregular Boundaries

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.

[@ozzyfromspace]

"Make a fine mesh and eat a sandwich while it's running"
You're so wise, Jacob-san 😂🙏🏾🕊️✌🏾

[@dimRizo]

Jacob, you are the man!! Thanks!

[@miscellaneous4195]

You wrote wrong equation but came up with the right one at the end. You Need to change negative to positive in equation d2T/dx2 (+) d2T/dy2 = 0

[@imrulkayesharu8610]

Can you please upload a video solving problems relating this formula?

[@king0vdarkness]

Awesome video! Much easier to understand, thank you! Please can I ask how you would find alpha 1 (if alpha 2 and delta x are defined)?

[@king0vdarkness]

Actually no worries, just found out you can use Pythagoras to find out values of alpha and beta

[@tugced7506]

thank you so much sir

[@jAys92L]

Hi there , your teaching is nice. however i wonder how should i determine the alpha 1 and beta 1??

[@kvyi]

alpha and beta refer to lengths. They are measurements based on the geometry of the situation. To clarify, here's how it's done for the example above. Assume the curve shown is a circle centered in the middle of the plate. Let alpha1=beta1=1. This means the circle has radius 2*alpha1 = 2*beta1. The circle equation is x^2+y^2 = r^2. Let y=-1, since r=2, solving for x gives sqrt(3). Thus, alpha2 = sqrt(3)-1 = .732; beta2 is the same.

[@naviddavanikabir]

@6:22
why is the denominator divided by 2?

[@juniomoreiramatemati]

I have the same doubt...

[@SiriusBlack-qo3xi]

Navid Davani me too

[@kvyi]

You're adding them together and dividing by two, so the idea is that it's an average of the alphas times deltax (you can factor out the delta x if you want).

[@tarunsantosh8811]

Shouldn't denominator just contain alpha1*x as we are finding derivative of derivative between i-1 and i

[@anantgairola3394]

@@tarunsantosh8811 I was thinking that too. I wonder if someone (perhaps Jacob) could clarify that.