Welcome to the class website for the course Finite Difference Methods for Partial Differential Equations. The class will focus on numerical approximation of partial differential equations using finite difference approaches. The class will cover both mathematical foundations and practical aspects of effective implementation of such numerical methods. Many examples will also be discussed drawn from problems arising in the sciences, engineering, and finance. For more details see the syllabus and the topics listed below.

Please be sure to read the prerequisites and grading policies for the class.

Selection of Topics

• Introduction to Finite Difference Approximation.
• Hyperbolic, Parabolic, Elliptic Classification of Second Order PDEs.
• Finite Difference Methods for PDEs from each of these classes (Hyperbolic, Parabolic, Elliptic).
• Multistep Methods.
• Convergence and Consistency.
• Stability.
• Courant-Friedrichs-Lewy Condition.
• Lax-Richtmyer Equivalence Theorem.
• Fourier Analysis / Von Neumann Analysis.
• Order of Accuracy of Methods.
• Solving Sparse Linear Systems.
• Iterative Methods.
• Fast Poisson Solvers via FFT and Multigrid.

For more information see the syllabus Δ.

Prerequisites:

Ordinary Differential Equations, Partial Differential Equations, and Linear Algebra.

Grading:

The grade for the class will be based on the homework assignments (see policy below), midterm exam, and final project as follows:

Homework Assignments 30%
Midterm Exam 30%
Final Project 40%

Homework Policy:

Assignments will be made weekly and posted on the class website. Prompt submission of the homework assignments is required. While no late homework submissions will be accepted, one missed assignment will be allowed without penalty. While it is permissible for you to discuss materials with classmates, the submitted homework must be your own work. The assignments will consist of a combination of analytic problems and numerical calculations. Basic programming in Matlab/Octave may also be required for some assignments.

Exams:

A midterm exam will be given in the class on Thursday, May 5th.

Final projects will be announced toward the end of the quarter.

Supplemental Class Notes:

GNU Octave Software and Documentation
Octave Software (Binaries from SourceForge.net)
GNU Octave Tutorial
GNU Octave Links (Tutorials and other Information)
Ubuntu (Linux Operating System) [Maybe useful to install dual-boot for running Octave]

Matlab Software and Documentation

Python for Scientific Computing (NumPy)

Explosion of the Ariane 5 Rocket (Consequence of Faulty Numerics)
The Sinking of the Sleipner A Offshore Platform (Consequence of Faulty Numerics)

Class Annoucements:

• No office hours on Tuesday, May 17th.

Homework Assignments:

Turn all homeworks into my mailbox in South Hall 6th floor by 4:30pm on the due date. Graded homeworks will be returned in class.

HW1: (Due Thursday, April 7th) (First Edition : Problems PDF Δ) 1.1: 1, 3, 4; 1.2: 1, 2; 1.3: 1abcd, 2.
HW2: (Due Thursday, April 14th) (Second Edition) 1.3: 3, 4; 1.4: 1, 4, 5; 1.5: 1, 2, 3, 4.
HW3: (Due Tuesday, May 3rd) (Second Edition) 2.2: 1, 4, 5, 6, 7; 2.3: 3; 3.1: 1, 3, 5, 6.
HW4: (Due Tuesday, May 17th) (Second Edition) 3.2: 1, 5; 3.5: 2, 8, 10; 4.1: 1, 2.
Final Project: (Due Monday, June 6th in my mailbox in South Hall 6th floor by 4:30pm).

---

Edit: Main | Menu | Description | Info | Image | Extras || View Extras | Log-out