Fall 2019 - APMA 922 G100

Numerical Solution of Partial Differential Equations (4)

Class Number: 4138

Delivery Method: In Person

Overview

  • Course Times + Location:

    We 10:30 AM – 12:20 PM
    AQ 5006, Burnaby

    Fr 10:30 AM – 12:20 PM
    AQ 5007, Burnaby

Description

CALENDAR DESCRIPTION:

Analysis and application of numerical methods for solving partial differential equations. Potential topics include finite difference methods, spectral methods, finite element methods, and multi-level/multi-grid methods.

COURSE DETAILS:

This course provides an introductory overview of the numerical analysis of differential equations, covering the derivation and theoretical background for the methods as well as their computational implementation.  A tentative course outline is as follows:  

Finite differencing (2.5 weeks): explicit and implicit discretizations; local and global errors, consistency, stability and convergence; treatment of boundary conditions; higher-dimensional elliptic problems, Poisson’s equation  

Spectral methods (2.5 weeks): discrete Fourier transform and FFT, spectral accuracy; Fourier and Chebyshev spectral methods  

Finite elements (2.5 weeks): two-point boundary value problems, introduction to theory, Poisson’s equation  

Initial value problems (2 weeks): Runge-Kutta and multistep methods, zero-stability and absolute stability, stiffness  

Parabolic equations (1 week): heat equation, discretizations; accuracy and stability, von Neumann error analysis, Lax equivalence theorem  

Hyperbolic equations (1.5 weeks): advection equation; leapfrog, Lax-Friedrichs, Lax-Wendroff and upwind schemes; CFL condition; modified equations  

Mixed and nonlinear PDEs (1 week): fractional step methods, IMEX methods, pseudo-spectral methods, exponential time differencing

Grading

  • Four homework sets (equally weighted) 40%
  • Take-home exam 20%
  • End-of-term-project (1/3 of grade is oral presentation, 2/3 for project report) 40%

Materials

REQUIRED READING:

Randall J. LeVeque, “Finite Difference Methods for Ordinary and Partial Differential Equations”, SIAM   (we will cover most of this book)

RECOMMENDED READING:

Material will also be drawn from other books, several of which will be available in the library reserves.  In particular, significant parts of the course will largely be based on chapters from the following texts:

- Lloyd N. Trefethen, “Spectral Methods in MATLAB”, SIAM

- Arieh Iserles, “A First Course in the Numerical Analysis of Differential Equations” (2nd ed.), Cambridge University Press

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS