Lecture -- Introduction to 1D Finite Difference Method

This video introduces the finite-difference method and how it is used to solve ordinary differential equations. The video covers how the finite-difference method is taught conventionally and then covers an improved technique for implementing the finite-difference method that is much simpler and leads to code that is more compact and more easy to read and follow.

[SoumilSahu]

This series is absolutely amazing. Thank YOU for giving these out to the world for free

[amiralizadeh]

it's been the best video that I watched about solving an ODE with FDM.

[rajnimoona]

In the improved finite difference method, how did you get the same matrix? if we have to follow the same process then what is the difference between the two. Also, i did not understand how you computed the boundary values for the column vector which was all zeros. I am sorry that my questions are too basic but I am really trying to understand.

[bvramaiah]

Excellent ❤️ awesome, thank you sir..

[mohammadabdelrahman]

A quick question professor, couldn't we just have right from slide 9 wrote the discrete form for the first derivative using the central difference method?

Or did you make the extra steps (slide 10) just to notify us about the unstable formulation?

btw thank you for this course, I'm starting to understand a lot of things. It's taking time, but I'm getting there. Step by step

[dieu-donnewandaogo]

Hell Prof. Thank you for such a splendid tutorial vedio. This has has truly helped me soo much. A quick question please. How would a periodically grooved wall boundary be incorporated with the FDM discretization?

[thongsmile]

Professor can you make video about to finite difference analysis of a linear elliptic equation in 1d

[mohammadabdelrahman]

what is making the finite difference so hard to learn is that every single source teaches it differently and uses different mythologies, you'd think that they're teaching a whole new different topic.

@CEM lectures do you have any advice when facing such problems, I'm studying these method for CFD purposes, but it is so hard trying to understand it when literally I'm required to read so many resources and it all gets mixed up :/

[doods]

what if the DE is non-linear there is a y^2 term in DE for example... And also what if you got condition on the derivative but the differential equation you're working on does not include y' for example what if your equation is in the following form y''+y^2=0 with one of the BC y'(0)=1