Lecture 35 - Explicit and Implicit Methods

Numerical Methods and Programing by P.B.Sunil Kumar, Dept of physics, IIT Madras

Category:

Education

Tags:

• Explicit
• and
• Implicit
• Methods
• for
• Partial
• Differential
• Equations

[msrasras]

Excellent work, thank you sir

[Perulaiz]

o look...0..

1 dislike.

[amilagmail]

thanks. best i could found in internet

[hyperzzip]

what kind of program did the professor use?

[hfcell]

The tridiagonal matrix is actually a Toeplitz Matrix. The most prominent property of the Toeplitz operators is that their eigenvectors are sines and cosines (or complex exponentials). This particularly means that Toeplitz matrix, A, can be diagonalized by a Fourier operator (e.g. DFT matrix), F: A = F-1 Λ F, thus reducing the transform complexity from O(n2) to O(n log n), which is the Fast Fourier transform limit.

[soonerufo]

Thank you for sharing this video. Very easy to follow. I appreciate it

[whatever3009]

these IIT professors have a very boring way of teaching with a monotonous tone, I expect them to be somewhat enthusiastic, I am not questioning their intelligence and knowledge I have no doubt they are very smart, but in these videos they sound so boring that they put me to sleep, look at Walter Lewin and how he teaches with such high energy.

[edisonlly19881105]

i will having my numerical method exam in two days time. from zero, u make me fully understanding PDE.. God bless you!! and thanks so much =)

[rekenmonster]

A clear explanation.

However, computing the inverse of a tridiagonal matrix is not necessary, one should retain the LU decomposition and solve LUx=f like Lz=f and Ux=z. This has two advantages:

1. The number of parameters to remember is about 2N (instead of N^2 for the inverse.

2. Calculation of x takes about 4N operations instead of N^2.

[golu22in]

thanks a lot.