The Finite Difference Method (1D)

This video explains what the finite difference method is and how it can be used to solve ordinary differntial equations & partial differential equations.
Contents:
- What is the finite difference method
- Calculating finite difference coefficients and setting up the equations
- Splitting up a domain into finite differences
- Applying forward, central, and backwards differences
- How to calculate the finite difference coefficients
- How the approximation changes with both step-size and order
Future videos in this series will include:
-Solving non-linear ODEs and PDEs with iterative methods
-Solving 2D problems with Dirichlet and Neumann boundary equations
-Solving physics equations such as the heat equation with non-uniform material properties

[@AJ-et3vf]

Very informative video, especially showing the difference between the accuracy of mixed and constant high order accuracy methods.

[@EmmanuelOseiTutu-n7v]

Great lecture!!

[@baranyagc5280]

Great work, thank you! But you should seriously consider changing the "apocalypse siren" sound in the background...

[@edu.sbsantos]

I liked !

[@HumbertLaxness]

Yeah I also really liked it, it adds an apocalyptic ambience.

[@mehmetfurkanceylan]

finally all makes sense. thanks for clear explanation

[@ARBB1]

Great work

[@stanislavpolzer1347]

So I finally learned that, using your explanation, thanks. Just a minor thing though: there is a typo on slide in time 7:50. The resulting value for f(1.75) is actually 15.8594 not 115.8594.

[@speedbird7587]

Nice video. I enjoyed and liked it.

[@ValleysOfRain]

You mention the boundary conditions here, but only give the setup for Dirichlet boundary conditions (i.e. y(x_0) = c1, y(x_n+1) = c2 ) - could you also describe the process for working with Neumann (y'(x_j) = some value) and Robin (y(x_j)+y'(x_j) = some value) boundary conditions?

[@AJ-et3vf]

Great video. Thank you!

[@sebinxavier2496]

Great video

[@theopaltarot]

❤

[@JamesVestal-dz5qm]

Were doing 1D finite difference method along the length of the reactor. Can I phone a smart friend? Your future president is getting creamed by the school right now!

[@StepStudyGymnasium]

5:57 what happened there exactly?

[@ifebunandujoshuaumeh5881]

Great work!

[@4_Gatitos]

Hello! Is there a way we could send you an email?