ONE-DIMENSIONAL DIFFUSION EQUATION SOLUTION METHODS. 1) Explicit Method is CONDITIONALLY stable because with too large time-step, the scheme will blow up. 2) Implicit Method is UNCONDITIONALLY stable irrespective of time-step but every time revolution step requires solving matrix equations 3) Crank-Nicolson Method: is the MOST popular method averaging the explicit and implicit methods; it has the advantage of the implicit and a resulting fast algorithm tri-diagonal matrix equations system (easy to solve) Thank you Sir!
2:34 "Both the time stepping and the space stepping become 2nd order". I don't see how the time stepping became 2nd order. In lecture 69 it was still 1st order. Can anyone explain?
Transposing a matrix has nothing to do with geometry. It simply means interchanging the rows and columns of a matrix, so that the first row becomes the first column, the second row becomes the second column, etc. For many matrices the transpose is also the inverse, so often taking the transpose of a matrix is a good way to invert it.
How do you actually compute the result here? Given that you don't know what U is to start it seems like you have an unknown on both sides of the equation
ONE-DIMENSIONAL
DIFFUSION EQUATION SOLUTION METHODS.
1) Explicit Method is CONDITIONALLY stable because with too large time-step, the scheme will blow up.
2) Implicit Method is UNCONDITIONALLY stable irrespective of time-step but every time revolution step requires solving matrix equations
3) Crank-Nicolson Method: is the MOST popular method averaging the explicit and implicit methods; it has the advantage of the implicit and a resulting fast algorithm tri-diagonal matrix equations system (easy to solve)
Thank you Sir!
2:34 "Both the time stepping and the space stepping become 2nd order". I don't see how the time stepping became 2nd order. In lecture 69 it was still 1st order. Can anyone explain?
The time stepping becomes a centered difference, which is second order.
@@ProfJeffreyChasnov So, does this mean then that when one averages the first derivative of two steps, it automatically becomes second derivative?
Same question
I am interested in seeing you to prove that the Crank-Nicholson method is unconstitutionally stable.
What were the initial and boundary conditions? u=0 at j=1 and 4; and u = 1 at l=0? They were not mentioned in the lecture.
Respected sir , could you please say the geometrical intuition/ interpretation of TRANSPOSE of an MATRIX?
Transposing a matrix has nothing to do with geometry. It simply means interchanging the rows and columns of a matrix, so that the first row becomes the first column, the second row becomes the second column, etc. For many matrices the transpose is also the inverse, so often taking the transpose of a matrix is a good way to invert it.
Hello Sir is there the possibility you can help me with a project in which I will need to use BTCS for a heat transfer problem ?!
Thanks for the video, I could solve my problems.
Great videos. Can I ask how or what is used to write on the screen?
Guassian elimination at the end wouldnt be computational expensive ?
Yes, it is. In those cases, we can use Crout's algorithm, which is less expensive and converges faster than Gauss's.
Excelent!! How do You write on the board??
Sir, it will be a long time since any of your videos have been uploaded. I miss you
Sir, can you please explain the CNM for the 2DBurgers' Equation.
Sir Plzzz can u tell the dimensions of light board u use and the name of mic
thanks for the videos Jeff, great information!
awesome series sir...
How do you actually compute the result here? Given that you don't know what U is to start it seems like you have an unknown on both sides of the equation
Initial condition is given.
@@ProfJeffreyChasnov I'm sorry I still don't think I understand how to perform the iterative process. Is there an example somewhere I could see?
Is this in coursera too?
Yes, sorry. It was private by accident and I just made it public.
thanks sir . what is the name of technology you used ? how do you sho yourself like this ?
It's called a light board.
Sir Plzzz Upload Videos About Quantum mechanics Mathamatical Model
Thank you very much sir for this.