Simon Fraser University
Engaging the World

Course Outlines

Spring 2024 - APMA 922 G100

Numerical Solution of Partial Differential Equations (4)

Class Number: 7364

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 8 – Apr 12, 2024: Tue, 2:30–4:20 p.m.
    Burnaby

    Jan 8 – Apr 12, 2024: Thu, 2:30–4:20 p.m.
    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:

  • ODEs - Initial Value Problems - Review 
    • Runge Kutta methods
    • ODEs, Euler's method, Taylor methods, Runge Kutta
    • Linear Multistep methods
    • Stability, Consistency, Convergence
  • ODEs – Two-point boundary value problems - Review
  • Fourier Analysis 
    • Fourier transform
    • Discrete Fourier transform
  • Time-dependent PDEs 
    • Finite difference formulae
    • Method of lines
    • Finite differences and Fourier analysis
  • Accuracy, stability and convergence 
    • Lax Equivalence
    • The CFL condition
    • The von Neumann condition
  • Spectral Methods  
    • Periodic boundary conditions 
    • Polynomial interpolation and orthogonal polynomials
    • Polynomial spectral methods
  • Elliptic PDEs 
    • Laplace equation 
    • Finite differences 
    • Sparse systems and Iterative methods 
    • Preconditioners 
    • Multigrid methods

Grading

  • Homework Zero 5%
  • Homework 35%
  • 2 quizzes 40%
  • Project 20%

NOTES:

Homework: a mix of theoretical and coding exercises. While you are encouraged to work in groups, I must be convinced that the work you hand in is mostly your own.

Project: The course project will consist of a written report and a presentation to the class. The report must be handed in prior to the presentation.

There is no final exam.

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

Typed lecture notes will be made available on Canvas

RECOMMENDED READING:

Finite Difference Methods for Ordinary and Partial Differential Equations
Randall J. LeVeque, siam
ISBN: 9780898716290

Spectral Methods in Matlab
Lloyd N. Trefethen, siam
ISBN: 9780898714654

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

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:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website 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