Spring 2026 - APMA 922 G100
Numerical Solution of Partial Differential Equations (4)
Class Number: 5254
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 5 – Apr 10, 2026: Tue, Thu, 2:30–4:20 p.m.
Burnaby
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Instructor:
Steven Ruuth
sruuth@sfu.ca
1 778 782-4452
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:
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Initial value problems: Runge-Kutta and multistep methods, zero-stability and absolute stability, stiffness
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Finite difference methods: explicit and implicit discretizations; local and global errors, consistency, stability and convergence; treatment of boundary conditions; higher-dimensional elliptic problems, Poisson’s equation
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Spectral methods: discrete Fourier transform and FFT, spectral accuracy; Fourier and Chebyshev spectral methods
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Finite elements: two-point boundary value problems, introduction to theory, Poisson’s equation
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Parabolic equations: heat equation, discretizations; accuracy and stability, von Neumann error analysis, Lax equivalence theorem
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Hyperbolic equations: advection equation; leapfrog, Lax-Friedrichs, Lax-Wendroff and upwind schemes; CFL condition; modified equations
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Additional Topics (time permitting): fractional step methods, IMEX methods, pseudo-spectral methods, exponential time differencing, iterative methods for elliptic equations.
Grading
- Homework sets 40%
- 2 Quizzes 30%
- End of Term project (1/3 of grade is oral presentation, 2/3 for project report) 30%
Materials
MATERIALS + SUPPLIES:
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:
RECOMMENDED READING:
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
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
At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.
To learn more about the academic disciplinary process and relevant academic supports, visit:
- SFU’s Academic Integrity Policy: S10-01 Policy
- SFU’s Academic Integrity website, which includes helpful videos and tips in plain language: Academic Integrity at SFU
RELIGIOUS ACCOMMODATION
Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.