Math 579. Computational nonlinear waves. Fall 2021.



Section 001. TR 08:00-09:15. Room: SMLC 120. Syllabus for Math 579 (69049). UNM required extra language for Syllabus. No book for the course.
Some interesting methods can be found in
"Nonlinear Waves in Integrable and Nonintegrable Systems" by Jianke Yang.
Table of content and preface.
"Chebyshev and Fourier Spectral Methods" by John P. Boyd.
Available on Amazon for <$28.

Office hours:

TR 10:15-11:30. Room: SMLC 220 or via Zoom by request.

How grades are assigned?

Completely HWs based.

Homework regulations

HW has to be typed in what ever editor you like.
If you were asked to produce any output -- it has to be copied in the HW text.
If you were asked to plot something, this plot has to be printed.
Essentially, it is recommended to type all HW together with plots and cut-and-paste outputs.
HW # Homework problems Due date
5 Homework 05 (Extra points!). December 14th, 2021, end of day.
4 Homework 04. December 2nd, 2021, end of day.
3 Homework 03. November 23rd, 2021, end of day.
2 Homework 02. October 21st, 2021, end of day.
1 Homework 01. September 16th, 2021, end of day.

Below you can find additional material.
Week # Extra material.
YouTube playlist for lectures' recordings.
15-16 Lecture 29 (zoom recording).
Derivation of equations for the wave in 3D case.
A chapter from J.Yang book. You need sections 7.2.1 (Petviashvili method) and 7.2.4 (Newton's-CG method).
Lecture 28 (zoom recording).
13-14 Paper with description of the 2D hydrodynamics equations.
11-13 Paper with description of the sweep method for Sturm-Liouville equation (Appendix C).
7-10 Paper with description of the split-step method for gas pipes.
4-6 Paper on some numerical methods for NLSE, including split-step.
Paper with more general consideration of split-step method.
FFTW (Fastest Fourier Transform on the West) library.
1-3 Different numerical integration rules.
Error analysis of integration rules.
Composite numerical integration rules.