Numerical Analysis 2 with Prof. Ringland
Project options: classic papers on numerical solution of a PDE
To access papers behind a paywall, go to library.buffalo.edu and search there. You will be prompted to sign in, and then you'll have access to all the journals to which UB subscribes.
#1
The discovery of solitons: reproduce the results of this classic paper by Zabusky and Kruskal. Make the best pictures you can - you have better technology than they had!
#2
Time-dependent Schrodinger equation: reproduce these quantum-mechanical scattering experiments of a particle hitting a barrier. Make the best pic tures you can - you have better technology than they had!
#3
Spontaneous spatio-temporal patterns in a chemical reaction: generate an interesting movie of a solution of this reaction-diffusion equation.
#4
Something else of particular interest to you - discuss with me ASAP.
Office hours
Wednesdays 3:00-3:50pm in 206 Math Bldg.
Class policies and logistics
Chalkboard photos and illustrations
| Day 1, Jan 23 | |
| Day 2, Jan 28 | Day 3: boards, Jupyter notebook |
| Day 4, Feb 4 | Day 5, Feb 6 Thm 7.4, Taylor |
| Day 6, Feb 11 Taylor series method with sympy board, code | Day 7 Feb 13 RK methods |
| Day 8, Feb 18 stability, LMFs notes, code | Day 9, Feb 18 LMF dynamics notes, demos |
| Day 10, Feb 25, implicit method, BVP shooting, boards etc, code 1, code 2 | Day 11, Feb 27 nonlinear BVP, code |
| Day 12, Mar 4, Exam 1 review, boards etc | Day 13, Mar 6, Exam 1 |
| Day 14, Mar 11, BVP by finite differences starter code, code written in class, boards | Day 15, Mar 13, BVP by collocation |
| Spring Recess | Spring Recess |
| Day 16, Mar 25 Galerkin boards, code | Day 17, Mar 27 Galerkin , boards, cubic bspline code, hat code |
| Day 18, Apr 1 PDE boards | Day 19, Apr 3 heat equation boards and results, heatmap code |
| Day 20, Apr 8 heat eqn cont'd boards, code | Day 21, Apr 10 wave eqn boards, eigenvalue code, solver ipynb, solver code, waterfall code |
| Day 22, Apr 15 Exam 2 | Day -6, Apr 17, FD convergence, elliptic boards |
| Day -5, Apr 22 boards, Poisson direct solve code, poisson_jacobi.py | Day -4, Apr 24 GS, SOR, boards etc, sor_eigenvalues |
| Day -3, Apr 29 boards, notebook 1, notebook 2, piano low F | Day -2, May 1, boards, 538_s25_day_27.ipynb, advection_fd_and_spectral.ipynb |
| Day -1, May 6 boards, code |
Homework
Please provide me with each homework as a single pdf. Pages of the pdf can be digitally generated, or photos of handwritten work, etc.
Any time there is a coding component, please ALSO upload your code - either as a Jupyter notebook (.ipynb) file, or plain text python.
| assignment | due | solutions |
|---|---|---|
| Homework #1 | due 11:59pm, Friday, Feb 7 | solutions |
| Homework #2 | due 11:59pm, Friday, Feb 21 | solutions |
| Homework #3 | due 11:59pm, Friday, Feb 28 | solutions |
| Homework #4 | due 11:59pm, Friday, Apr 4 (p1 hint) | solutions |
| Homework #5 | due 11:59pm, Friday, May 9 | solitions |
Gradesheet
Scores will be emailed individually.