MATH 6630-01 — Numerical Solutions of Partial Differential Equations
Spring 2023
| Instructor: |
Akil Narayan |
| Email: |
akil sci.utah.edu |
| Office phone: |
+1 801-581-8984 |
| Office location: |
WEB 4666, LCB 116 |
| Office hours: |
Mondays 1:30pm-2:30pm (LCB 116), and Thursdays 12pm-1pm (WEB 4666) |
| Class meeting time: |
Monday, Wednesday 11:50am - 1:10pm |
| Class meeting location: |
AEB 360 |
Analysis and implementation of numerical methods for solving partial differential equations. Issues of stability and accuracy. Linear and nonlinear problems.
The course syllabus is here: PDF
The content of this course is split across this website and Canvas. The material available on this website is:
- Course syllabus
- Project assignments
- Course slides
- Links to software
The material available on Canvas is:
- Course syllabus
- Grading results
Graded assignments
Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.
Homework assignments
Late work will not be accepted without advance approval from the instructor.
|
Problem set description
|
Due date
|
Homework
|
|
0 : Submission Practice
|
February 13, 2023
|
PDF
|
|
1 : Finite difference methods
|
March 3, 2023
|
PDF
|
|
2 : Spectral and finite volume methods
|
April 26, 2023
|
PDF
|
Miscellaneous handouts
The following are various relevant handouts.
|
Description
|
Posting date
|
Download
|
|
Presentation information and a non-comprehensive list of papers
|
March 31, 2023
|
PDF
|
|
Homework submission instructions
|
January 28, 2023
|
PDF
|
|
Course introduction and logistics
|
January 9, 2023
|
PDF
|
|
Notation and PDE basics
|
January 13, 2023
|
PDF
|
|
Finite difference for 1D stationary problems
|
January 23, 2023
|
PDF
|
|
Finite differences for Laplace's equation
|
January 23, 2023
|
PDF
|
|
Initial value problems, I
|
January 25, 2023
|
PDF
|
|
Initial value problems, II
|
January 31, 2023
|
PDF
|
|
Initial value problems, III
|
February 6, 2023
|
PDF
|
|
Initial value problems, IV
|
February 8, 2023
|
PDF
|
|
Finite differences for parabolic problems, I
|
February 15, 2023
|
PDF
|
|
Finite differences for parabolic problems, II
|
February 22, 2023
|
PDF
|
|
Finite differences for parabolic problems, III
|
March 13, 2023
|
PDF
|
|
Fourier Series
|
March 13, 2023
|
PDF
|
|
Fourier Interpolation
|
March 15, 2023
|
PDF
|
|
Weighted residual methods
|
March 24, 2023
|
PDF
|
|
Fourier spectral methods, I
|
March 28, 2023
|
PDF
|
|
Fourier spectral methods, II
|
March 29, 2023
|
PDF
|
|
Orthogonal Polynomials
|
April 9, 2023
|
PDF
|
|
Polynomial spectral methods
|
April 13, 2023
|
PDF
|
Software
The following are links to software used during class demonstrations.
|
Description
|
Language
|
Download
|
|
Code for in-class demonstrations
|
Python
|
github
|
Resources
|