Finite Difference Method for Solving ODEs: Example: Part 2 of 2

[nnostalgy]

very important , thanx very much

[a4b3c2d1e0f]

Awesome, thank you ! :D

I did homework 1 and got the following results:

u1 = 0.008

u2 = 0.004906

u3 = 0.003646

u4 = 0.003

which is pretty cool to see just how using a centered difference formula can improve accuracy.

[TimChoi89]

Thank you so much for your videos. You're a great help!

[erol1991]

how did he just get the exact solution??

[numericalmethodsguy]

@erol1991 One gets the exact solution by using Frobenius series. Assume u=summation of a(i)*r**i, with i going from -infinity to +infinity. Substitute in the ODE and you will see that only for i= -1 and i=+1, the coefficient is nonzero. Then apply the boundary conditions (see numericalmethods(.)eng(.)usf(.­)edu - click on keyword, click on Finite Diff Method for ODEs, see the example in the textbook chapter)

[samia7756]

now i hope i can remember all this during the quiz. inshAllah!. thanks again



[kingangustheh]

Thanks so much for this. I suspect your videos are going to be the only reason for me getting though my 2nd Year EMTH paper. Keep up the good work.

[Onias]

Thank you very much for putting up this video, it has been immensely helpful.

[Jeanpaul1011]

You mentioned that Gauss-Seidel converges if Diagonally Dominant, i thought only Jacobi method converges if Diagonally Dominant, it is not guaranteed for Gauss-Seidal